I have avoided this post for some time - mostly because the answer is rather personal preference. I have written around the topic plenty - in posts like "So You Want to Start Tying Flies". I have advised that fly tying to save money is probably a mistake. Hell, I have given my thoughts on scissors. In two and a half years, why has this rather dedicated fly tyer not given their thoughts on vises? It is a no-win situation - so be prepared that I will not get it right, but I will try my best. More than anything, I will share a lot of links and videos to give you a diverse perspective.
What I like in a vise, may not be your personal preference and your favorite may not be something that works as well for me. It is, to make an analogy to my high school days in small town Wisconsin, a Ford/Chevy/Dodge truck fight. People prefer one brand over the other for reasons that are sometimes rational, sometimes not so rational. I avoided those fights too - mostly because I did not give a shit - I have never been a vehicle person. How much one person is willing and able to spend is another significant variable. Your favorite vise may not fit another person's budget. Vises range in price from sub-$20 vises to those that are $700 or up. LAW (Lawrence A. Waldron) vises have sold, used, for over $3,000. Not everyone can, wants, or "needs" to tie on the best vise ever made - whatever your or their opinion of that is, is.
I have also hesitated to write a post on vises because it has been done a ton of times - see the list at the end of this post. I am not treading new ground but I come with a different set of experiences and the willingness to share a lot of links to other posts and videos on the topic.
My Vise (Vice?) History
I start here because vises are quite personal and what I have most experience on, what I like and do not like in vises informs this post and will ultimately be how you probably choose what vise you buy or what vise you now own.
My first vise was a Regal vise (video review), as many others first vises were. It was a really good vise. Back in the day, rotary vises were just becoming more commonly used. This was over thirty years ago so that is probably not the model they make any more but it would be equivalent to "Regular Vise Head". It was not a true rotary vise but it did allow you to rotate the head and look at the other side of the hook. I really liked this vise and it was not the base level at that time - which was probably the Thompson Model A - but a pretty significant step up. This is not to say that the Thompson or others like it are poor vises but that there are better vises for most people.
My next vise was Pamola Fly Lathe - which at the time I paid a lot of money for - over time, I figured out that I did not like any more than my Regal. It was a nearly true rotary vise - but not really what I was looking for. I sell very little gear that I own but I sold this and went back to my Regal, as best as I can remember. I liked my Regal vise a lot but it is, in my opinion, a better vise for tying large flies than it is for tying small flies. And I had the "jaw issue" that a lot of Regal users have experienced - they chipped when a hook went flying out of the vise (I would argue through bad luck, no fault of my own). What Regal users - including myself - love about Regal vises is that they are quick and simple to use and hold (larger) hooks incredibly well. The downsides of the Regal is that it gives you little control and little access to small hooks.
Some time later, I bought the LAW vise I tie on today and have been for the last twenty-plus years. Yes, it was a hell of a splurge at the time for someone that really could not afford it at the time but I am down to where the vise has cost me less than $30 a year. And seeing that I have tied an estimated 12,000 flies on it, that is a bit more than a nickel a fly. What I love about the LAW is that it is simple and purpose-built. There is a comfortable place for my off hand, it will tie flies from as small as you can tie to nearly as large of streamer and saltwater hooks as there are. (I say "nearly" because a friend gave me 9/0 shark hooks that are too thick to fit into the jaws.) And it fits this range of hooks without needing to any adjustments. It fits my tying philosophy - vises should be simple and not require much futzing around. I do not want to have to make adjustments in jumping from tying a few streamers to a few midges. It is a great vise but it is no longer made and is quite expensive. There are however a few vises that use the same jaw design which I will talk about later.
I have played around with a number of friend's vises, but never tied enough on them to fully understand what I think are the pluses and minuses of each. For a relatively inexpensive vise, the Danvise (video review) was pretty impressive if you can get past the plastic aesthetic. The working parts are, of course, metal. I've tied on a variety of Renzetti, Dyna-King, Peak, Griffin, Thompson (no longer produced, as best as I can see), HMH, Wolff / Atlas, Snowbee, Norvise, and other brands. I have a have cheap Cabelas vise that came with a tool kit - it is what you would expect of a what is now a $40 kit.
What to Look for in a Vise?
There is no perfect vise - every vise has its strengths and its flaws. The best vise for you - there probably really is not only one - is the one that fits your needs and tying style and your budget. Let's face it, budget is probably the most significant factor in the decision making. You can pay $20 to $50 for a vise or you can pay nearly $1,000 for a new Renzetti Master in Purple Popsicle. What you are willing to spend on a vise will dictate, to some degree, the bells and whistles but the basic goal - the basic need of every vise - is to securely hold a hook. Some of the less expensive do this less well or they give you poorer access to the hook they are holding.
Questions You Should Ask Yourself
Price - how much am I willing and able to spend? How much will I realistically tie? If tying is a major part of your life, spending around $1,000 on a vise you will use for 20, 30, or more years is not that "crazy". (Well, it's still a bit crazy...)
Fly size - what size flies am I going to be tying? Some vises hold large hooks better, some vises do not allow you as good of access to the hook as others which becomes a major issue on small hooks.
Rotary or stationary head - I see absolutely no reason not to have a rotary vise, even if you do not tie true rotary (more below). But there are a few fixed head vises that are less expensive if cost is your number one concern.
True Rotary - do I need a vise where the hook shank remains in the same place as I rotate the vise (true rotary) or am I happy with a vise that is not quite true rotary (the hook shank moves a bit) or do I just want to see the other side of the hook on occasion?
Base type - what does my fly tying area look like and does a pedestal or c-clamp work better for me?
The smaller the range of flies you tie, the easier it is choose a vise that works well for your purposes. There are even vises specifically to tie streamers, Spey and Dee flies, or Atlantic Salmon flies ("irons" - like the Peak LIRS) and those to tie tube flies.
Jaws
Jaws are the most important part of the vise - without a very good set of jaws, the other features really do not matter. Jaws are hardened - but not too hard - metal designed to securely hold a hook. They come in a variety of shapes and sizes but in nearly all of them, (nearly) parallel pieces of metal are brought together to hold a hook. There are essentially two different ways that jaws hold hooks - through a collet system where a one piece jaw is pushed or pulled together or through a lever system where two piece jaws are brought together. Most of the Renzetti vises use two piece piece jaws as do the LAW (and copies of it), Griffin, and Regal jaws. The Thompson Model A, Peak, and Dyna-King use the draw and collet system. Both systems can hold hooks quite well but generally the parallel jaws allow better hook access because the design requires less metal.
Aside from holding a hook well, a good set of jaws should provide ample access to your hook and if adjustable, be quick and simple to adjust. I do not much care for vises that I have to "futz" with (see video below) to get the jaws close to parallel so the hook can be clamped in them. It is the major reason that I think the LAW style of jaws is superior to others. While there are no new LAW vises being made, a number of manufacturers are copying that style of jaws. HMH's TRV (True Rotary Vise) and the FNF Talon Vise are two (rather expensive) options for that style of jaws. There are manufacturers that allow you to buy other jaws - or entire heads in the case of Regal - to tie different fly sizes. Again, more "futzing" than I care to deal with.
A tyer that ties a lot of streamers may look into Peak's Large Irons Retention System (LIRS) and those that tie a lot of tube flies may want a purpose-built vise rather than using the tools to allow you to tie tube flies on your normal vise. Tim Cammisa (Trout and Feather) has a video on a couple of tube fly models and an entire series on tube flies. If you tie a lot of Clouser Deep Minnows, Renzetti makes a vise for that.
In my experiences, Renzetti vises tend to offer quite good access to the hook; Peak and Dyna-King tend to require a bit more maneuvering to provide better hook access. I have less experience with the others to speak to them.
Pedestal or C-Clamp?
My personal preference is a pedestal but it has to be one that is heavy enough to serve its purpose - to securely hold the vise in place. Pedestals are more versatile - you can use them anywhere. Cheap, light pedestals suck and are generally the reason that some do not like pedestal vises. I would rather have a C-clamp than a small, light pedestal but I much prefer a heavy, wide pedestal which I think is much more convenient. Conventional wisdom is often that C-clamps are preferable for traveling but I disagree because you do not always have a table that accommodates a C-clamp.
Your preference for a C-clamp or pedestal depends a lot upon your fly tying set up. In a Kelly Galloup video below, he talks about his preference for a C-clamp. I prefer a pedestal because I tie on a flip down desk that allows me to get close to my vise, much like why he talks about preferring a C-clamp.
Rotary and True Rotary
Rotary vises allow you to see the other side of the hook while tying, to move the hook to place materials on different parts of the hook shank, and to wrap materials more quickly and accurately. I would not buy a stationary head vise as I like to be able to examine my fly when it is in the vise. How I am differentiating these terms is a stationary head does not allow you rotate the head at all while it is holding a hook, a rotary vise allows for a full 360 degree rotation of the jaws and hook, and true rotary mean that the hook shank remains in the same plane when the jaws are rotated. I like my true rotary vise but honestly use the rotary feature to wrap materials less than I should. In part, this is because I learned to tie on a Regal non-rotary but with a rotating head (i.e. not stationary). Just because you have the rotary feature, doesn't mean you always have to use it.
So What Vise Should I Buy?
I can not answer that question for you - there are a ton of variables and I can not spend your money. And again, it is a bit of a Ford/Chevy/Dodge fight - people have strong opinions based on their often quite limited experiences and own preferences. That is why I started this post with my own experiences and preferences.
I think Kelly Galloup does probably the best, most thorough job of explaining the tradeoffs in video form. Like most of his Slide Inn videos, the videos are long (these are really short for KG videos) and detailed. He does a good job of thinking through the considerations that should be made in choosing a vise. And he very clearly states that a more expensive vise will not make you a better tyer - only time and repetition will do that.
Like talking about fly rods, if you can, try before you buy. While a vise is a pretty significant investment, if you tie for decades on that same vise and fly tying is your major hobby, that investment is a pretty good one. And I know I am talking about spending other people's money but if I were a new tyer, I would not go with the lowest level vise as they tend to make tying a lot less easy and fun.
To me, the sweet spot, where you get a really good vise that is true rotary that you probably would never need to replace is around $200. This puts you into a Renzetti Traveler or a Peak rotary, probably the two most popular vises on the market. There are other good options around that price from manufacturers that have not been at it as long as Renzetti. Yes, $200 is a lot of money to spend, particularly if you do not know if you will stick with fly tying. At the same time, you can probably find a used vise on E-bay, your local fly shop or Trout Unlimited or Fly Fishers International buy/sell/trade event, or similar place - a quick search returned over 700 options.
My recommendations for those just getting into fly tying are that if I were tying mostly trout flies where I want to be able to tie a range of sizes but more on the smaller size, I would look at a Renzetti Traveler. If I had a knock on the traveler is that it does not look overly sturdy - but I have friends that have tied on them for dozens of years. If I were mostly a warmwater - bass, pike, musky - angler I would look to a Dyna-King. The Peak LIRS looks great but it is quite limiting to only tying streamers (effectively). Though Peak allows you to buy a head with normal jaws as well and you can move to that when not tying streamers. The tyer that has been at it and may want to upgrade from their starter vise has tons of great options and probably already has enough experience and opinions to choose their own upgrade - but do try the Waldron (LAW) style of jaws and see what you think. For me, the simplicity and not having to make any adjustments, change jaws, etc. is spectacular.
Links to Vise Video Reviews
These are just the ones I selected, there are other options out there. And these are the opinions of different people - your preferences and experiences may vary. Many of them are from Matt O'Neil and his YouTube channel, Savage Flies. He also did broader comparisons including 5 Fly Tying Vises under $50 and under $100 and others have done similar price comparisons - like for $200ish rotary vises or comparisons of "basic starter vises".