Here's three good pieces of information.
1) Yasuaki Fujita had absolutely no role in this. The only two Capcom SFC games he contributed to were Final Fight 2 and Breath of Fire. He also had absolutely no role in any of the Sega Genesis/Mega Drive games.
http://www.hcn.zaq.ne.jp/first_circl...n_shoukai.html
2) Toshio Kajino and Syun Nishigaki were the Sound Supervisors for the SNES version of Street Fighter Alpha 2. This tells me that, like the SNES versions of Street Fighter II and Street Fighter II Turbo, the original sound staff was involved to some degree. Whereas Isao Abe was definitely involved in both the arcade and SNES versions of SFII & SFIIT, Syun Nishigaki was definitely involved in both the arcade and SNES version of SFZ2. [I think Toshio Kajino only did sound effects for this one, as he usually does]
http://www.youtube.com/watch?v=kMWtEXLhUA4#t=15m10s
3) Street Fighter II: Champion Edition had similar sound staff amongst different versions of the game.
-The Genesis version had sound effects by Tatsuya Nishimura (same as SNES SFII games) and Tadashi Joukagi, who are credited in that same order for the Turbografx version.
-The Turbografx version also includes Sound Software Design Credits for Yoshihiro Sakaguchi and Yasushi Ikeda (same people and order as SNES SFII Turbo).
-As for the music design, it's definitely different between the two versions (Tadashi Joukagi, Setsuo Yamamoto for Genesis; Mari Yamaguchi, Isao Abe for Turbografx), but that just makes the Turbografx version even closer to SNES because of Abe's inclusion, even though he does a lesser share in Turbografx than in SNES.
http://www.youtube.com/watch?v=TFKBgMGpNf4#t=5m55s - Genesis
http://www.youtube.com/watch?v=TSsOYIqSegE#t=8m33s - Turbografx
So what does this mean for SSFII for SNES? I'd say Syun Nishigaki and/or Isao Abe worked on this just as they did the arcade version, as with the SNES versions of SFII and SFIIT. Perhaps Yuki Iwai also had a role in the music. Ippo Yamada's sound effect credit, however, is absolute.
As for SSFII for the Genesis, I'd say Ippo Yamada's sound effect [not sound program] credit carried over, just as Tatsuya's did for Champion Edition. As for music, It could be Setsuo again, if's he's as consistent as Isao is to the arcade and SNES versions.