OK, can't say regarding the WII versions, but here's my two cents assuming the 360 ones are similar:
Les Paul all the way for me at least. GWHT's is slightly bigger, and has the slide bar (which I almost never use anyway, cuz while it is cool at first, it's just a gimmick that doesn't help much, especially on expert). I don't like it's strum bar though, almost RB Strat styled, and that was a huge deal breaker for me. Please note that I play RB (RARELY GHWT) with it, so maybe if you prefer GHWT you might want that slide bar, idk. The Les Paul just feels overall sturdier and better, at least for me.