There are five kinds of vice jaw clamping systems I am aware of for holding hooks. You have included two under one heading, but from an engineering point of view they are significantly different.
Pull into collet, Push into collet, Spring, Two plates and a pivot. Loop and grove.
In my time tying flies I've owned the first 4, and tied on the last one.
Pull into collet type (Thompson and copies, HMH etc.) These hold the jaws under tension. Steel, which most jaws are made from is not at its strongest under tension. The quality vices overcome any problems by using materials that will stand up to the forces involved in fly tying. The failure points tend to be around the cam attachment and the hinge points at the bottom of the slot between the jaws. The repetitive bending at that point has been known to break jaws at the bottom of the bifurcation.
Push into collet (Dyna-King) The jaws are under compression so are stronger. The cam is not attached to the jaw and has a larger surface area of cam bearing the load.
Both these two kinds of vice have two distinct problems. They require the metal of the jaw to be bent during the jaw action. If quality steel is used this isn't a problem, the bending takes place within the elastic limits of the material. I have seen quite a few cheaper vice jaws that have broken at the bend point. The other problem is access to the insides of the jaws. Many years ago there was a debate over whether or not jaws should be hardened. It seems that all vice jaws are now hardened. With jaws that are made from 1 piece of steel access to the insides of the jaw, which is the load bearing surface, is restricted. This makes it much more difficult to harden the jaws well. These are all problems that are overcome by use of higher quality materials on better vices. They are, though, the usual fail points on cheaper vices.
Sprung Jaws (Regal and copies) limit the movement of the jaws by the size of the cam so you can not overstress them. The only problem they suffer is brittleness at the very tips of the jaws. Many people have pointed out that the jaws can be chipped with a small hook in the very tips of the jaws. Regal overcome this with the quality of material.
Two plates and a pivot. (Renzetti, LAW, J Vise etc.) This method gives the greatest mechanical advantage when clamping the hook. The plates do not bend as they act around the pivot. The way the hook is held is the same way a work piece is clamped to the bed of a milling machine. The forces used there thousands of times greater than in tying. As the jaws are made of separate pieces there is no problem accessing any area of the jaw to harden them.
Loop and grove (Smowbee AR vice etc.) Here a loop of metal pulls the bend of the hook into a grove. This is a novel idea but unfortunately not suited the the forces used in fly tying. Repetitive sideways movement loosens the hook. If you put a long shank hook into one of these vices and run down the hook shank with touching turns of thread you will pull the hook from side to side with teach turn. Do this moderately quickly, and the hook will loosen.
In choosing a vice my first consideration, before how the hook is held, is access to the hook. The dream would be this. Imagine fly tying being featured in an episode of Star Trek. There would be a small plate on the table top emitting some kind of force that held the hook in space 8 inches or so above it. You would have total access to the hook. That is the ideal vice, anything else is a compromise. As we can't do that yet it is a case of finding the best compromise you can find. It may well be different for you, than it is for me.