This is a more complicated issue than people usually think - depending on some factors, thumb behind the neck can make a lot of things a lot easier or it can make some things much more difficult or even dangerous AND the same is true for thumb high and wrapped around the neck.
In my mind, we can’t really isolate ‘parts’ because we have to look at the whole picture:
- where and how the guitar is being held (or if you’re standing and the guitar is on a strap), that is, which leg, which points of contact, height of chair, feet on the ground vs not, etc
- angle of the guitar neck relative to your body (the higher the angle, the more comfortable thumb-on-back will feel, and vice versa)
- angle of wrist, amount of space between palm and guitar neck, location of fretting-arm elbow, etc
and of course like @tommo alludes to, what material you’re trying to play makes a big difference. I advocate for a more classical position for most things at first then simply finding what’s comfortable for the player and going more so classical/neck up for things involving stretches and complex chords, and more so thumb wrapped/neck horizontal for things with lots of vibrato, bending, and/or left hand muting of strings.
Crucial thing though, if you play around with the thumb lower than you’re used to (ie on the back when you’re used to wrapping it over the top) make sure your wrist is pretty much neutral when you play, as it’s SO common for people to stick their wrist way out when trying to get bigger stretches, and IME it’s more likely to lead to cramping and pain issues.