Leg vise can be built from solely wood components and has a deep throat.
Yes, but actually any type of vice can be built entirely from wood if needed or desired (as many were in the past). It usually requires that the components are scaled up somewhat for needed strength, but in essence you're just substituting a threaded wooden dowel for any threaded steel rods, plain dowels for the alignment rods/bars and the jaws are just wood without having a metal plate or some sort.
It also is the largest of all bench vises from what I can tell.
Largest vice is arguably the end vice or one of the twin-screw vices commonly called a Moxon these days:
As you can see, these are quite a bit wider than you'd tend to see in a leg vice. But in all cases it does depend on the scale on which the vice is built. It's quite possible to make a smaller Moxon-style vice just as you can have wider or narrower versions of all vices.
What are the functional differences between a leg and front vise?
It terms of their utility I suspect the answer is actually nothing. They work similarly enough that they could be considered interchangeable. Or to put it another way, someone with either a face vice or a leg vice isn't lacking something significant that the other has.
What criteria might make me choose one over the other?
Honestly I think leg vices tend to appeal to people mostly based on their looks and their traditional style, rather than being a decision based primarily on functionality. Although the homemade aspect of them is also a major factor for some people; however it must be said, versions of all vices can be shop-made.
Now regarding the use you intend to put them to, as I say in my comment above, you can do dovetailing quite happily without any sort of vice if the bench design allows an alternate workholding method, such as the traditional holdfast (or a modern variation), as this extract from one of Chris Schwarz's books shows:
(Note you could also use a pair of holdfasts to hold the workpiece firmly.)
So if you're after the simplest possible option that allows you to hold a workpiece vertically something along these lines is it. You could also use quick clamps, parallel clamps or F-clamps to clamp a board vertically to one of the legs of your bench as a very quick and expedient variation (useful as it doesn't require your bench to have a front apron or any horizontal holes bored in the legs, so in theory this method is adaptable to nearly any bench).
However that's not the solution I think would best suit you. When I started writing my reply in the morning before I got called away I was intending to build towards a recommendation of a Moxon-style vice just as in grfrazee's excellent Answer.
One of the chief advantages of using a Moxon-style vice for dovetailing specifically is that you can raise the clamped height of the workpiece above the usual height of working:
Nearly any vice can hold a board vertical with its top edge at that same height but with a conventional one the clamping surfaces are right at the level of the workbench so the piece is held much further down its length. This of course allows for more vibration as you might get sawing dovetails. When doing dovetails on smaller boards, e.g. for small drawers and boxes, this raised clamping height really comes into its own, so that you're not doing fine, accurate sawing bent over in the same posture you used when planing a board face.
Another of the key advantages of this style of vice as I see it is that they can be built by the woodworker in so many different ways, so there's a version out there that would suit any budget. Some makers use commercial vice hardware for some or all of the working components, others just buy a type of threaded rod with a few matching nuts and go from there, and some make every component from wood:
Still others make the vice using nothing more than existing clamps:
As you should be able to see from the above picture the one made using F-clamps doesn't even require that the clamps be built permanently into the vice, so it's particularly useful for the woodworker with limited space or means.