If you want to compare handheld vs wrist then you need to compare the same release. Not sure how many manufacturers make same model in both setups these days (fletchmatic and fletchunter still do, excellent releases by the way). In most but not all cases a wrist release when compared to a handheld works better, but we are all different. The key is consistency, which one can you have a more consistent anchor point with.
I have been involved in archery for over 30 years now , I used to shoot Competition on a pro team all over the southeast and taught a lot of people how to shoot better. If I learned one thing, it was that no two people shoot exactly alike. There are the basics that you need to achieve but beyond that how you choose to get there is up to you.
When you shoot regardless of the method you need to be overall relaxed. Watch many of the pros you'll see them exhale nice and deep while focused on the target, inhale on the draw and slowly bleed air as the sights settle on target. When you shoot as many arrows as they do this becomes second nature. Now what do the rest of us part time shooters do. We look for things in our setup that will lead us to this relaxed state. If you are straining to pull that bow back, you aren't relaxed. If you have the habit of pointing at the moon then drawing the bow back you aren't relaxed. If either arm is shaking, you aren't relaxed. If you have a red face or a death grip in any part of your form you aren't relaxed. I would venture to say 40% of a shooters errors occur right here.
Now how does a wrist release help you with this. For most archers a wrist release will allow you to pull and hold a few more pounds maybe just enough to get to the bows sweet spot. It also allows you to pull with your arm instead of your hand, hand can stay relaxed. It doesn't matter as much for hunting but if you shoot tournaments, which archers hand would you expect to have worked less, the one that has been gripping a release or one that has only used that hand to bump a trigger.
if a wrist release is giving you problems, don't go totally re-working your form but try this for a few shots and see how it feels (we don't care where your arrows are hitting, just how does it feel, are you relaxed). Left arm bring bow on target but slightly high, draw the bow straight back and tuck your release hand thumb behind your neck, now relax as you settle in and Shoot on exhale or slight pause, do not move a muscle until you see that arrow has stopped moving in the target. Now lower the bow. Don't worry about peep, kisser or any other device alignment, don't change a thing. We are just checking the feel. Did that form feel better to you? Now try it with a handheld and compare.
If you do that exercise, you will know which method you prefer. I have only known about 30% that stay or go to handheld after that little exercise. They weren't wrong, what is right is not what Joe does, what's right IS what works for you. Long winded but maybe it'll help. I personally use the fletchunter, no matter if I'm slipping through the woods or sitting in the stand, it is attached to my loop and all I have to do is draw the bow, no looking down to connect it to the loop, it's already there. You can do that with handheld but in many cases you will have to look at the release to avoid bumping the trigger when you grab it therefore taking your eyes off the deer.
The others all brought out valid points in both cases and to me one of the most important features of a mechanical release other than few moving parts is an adjustable trigger.
