Best stick option for all next gen compatibility

If you’re not into modding WhatRShowers then perhaps the easiest way for you to go would be the Joytron stick mentioned (2 console compatible).

If you want to dabble in modding:
Owning an Xbox360 as opposed to PS3, if I recall correctly nets you 2 fighting games; a Dead Or Alive title and a Guilty Gear title. The latter can be easily amended via a ps2 emulator for PC or a first gen PS3.
The Wii nets you essentially Tatsunoko Vs Capcom, purported to be a great fighter (haven’t tried it personally).
So essentially fighting game-wise you want to fully support PS3 (which you have) and maybe Wii, Xbox360 or both meaning you could get away with an MC Cthulhu based custom stick further modded for support of either console.
MC Cthulhu is reported in the relevant thread as being ok for Wii games supporting GC controllers (including TvC). Perhaps you should check with Toodles, if you decide to go down this route.