The advantage of a thumb trigger over an index is the ability to remove your index finger from the equation. In other words they are harder to punch and therefore make it easier to shoot a bow closer to it's full potential........and that's a surprise release. That can only be achieved by shooting back tension.
Not saying that it's impossible to shoot an index release with back tension, it just takes a heck of a lot more discipline to do so, and more than I have from shot to shot.
If your current method of release doesn't mildly/pleasantly surprise you, your release arm isn't "Popping" backward at the shot, you are gripping the release body, or only your index finger moves at release,........then chances are you aren't shooting anywhere close to your accuracy potential.

Now......with all that said and we're all ready to round file our index releases, they (Thumb triggers)can have a decided disadvantage when hunting.
Sometimes a quick shot is necessary when hunting, where PINPOINT accuracy isn't necessary, shots where you NEED to punch a trigger to a degree. Thumb triggers make me nervous in a treestand for all their accuracy......they typically have very light no travel triggers, are slower to fire in a proper shot sequence, and if not connected to your wrist via some cord........you could drop it.[:-]

As much as I LOVE thumb trigger releases for target/3D.....that's all that I will ever use. I would never(Unless an emergency) use my thumb trigger releases for hunting.
I take that back.......I WOULD shoot one for Pronghorn.
I strive to shoot my index releases with back tension and a surprise release, but I am willing to give up my highest accuracy potential in favor of VERY GOOD accuracy in a more hunter friendly design that I get from an index release. I also want the option to MAKE the release go off EXACTLY when I need it to, and that's easier with an index.

My advice if you want to play.......get a good thumb trigger style. Learn to shoot it with back tension only. (The first bunch of shots are a treat.) See just how accurate they are, shoot some good 3D scores with it, and then learn how to shoot your index release with back tension for hunting.

Try the Tru-Balls I think their thumb triggers are OK, but they feel a bit clunky to me....I personally prefer Carter thumb trigger releases. They feel like butter in the hand, and have a model to fit pretty much any hand style or finger pattern you would like.
Head to a shop and ask to handle all of them.......one will stand out.
My personal favorites are the "Just Cuz" 3 finger, "Insatiable" 4 finger , or the "Target 4"