Genesis never had a version
Yeah it did.
Sigh...
Seriously, this discussion comes up every now and, and hardcore PCE pundits throw their sprite sheets around and express hatred for fruity SNES horn/guitar effects and then it all goes down for another couple of months. Basically people who don't actually know jack shit about Street Fighter talking endlessly about all the aspects of it that don't f*cking matter.
If you knew anything about SFII you'd know that this THE GENESIS VERSION IS TURBO. Its called "Special Champion Edition" to keep Nintendo happy. There is no arcade game called "Special Champion Edition". f*cking hell. I don't care what the box says, its Turbo. If Chun Li has a Kikoken that is stolen from Dalshim's Yoga Fire sprite...its Turbo.
SFII in the arcade was five games: SFII, SFII', and SFII'Turbo (all on CPS), Super SFII and Super SFIIX (aka: Super SFII Turbo) both on CPS2.
On consoles in the 16 bit days:
...there was only one version of SFII (SFC)
...there was only one version of SFII' (PCE)
Turbo was on MD and SFC
So was Super
Super Turbo was on nothing except 3DO and Marty until the PS1/Saturn era. Those systems got all five games.
And of the 16 bit conversions THEY ARE ALL VERY GOOD. SFII on SFC has some issues, but really it was very very good. None of them have "better control", they just have different controllers. A better controller is no better control.