The arcade equivalent had that title or a similar one and was the second version of SFII. Champion Edition added mirror matches and let you play as the 4 "boss" characters, Balrog, Vega, Sagat, and Bison. In the original version, Street Fighter II: The World Warrior, you couldn't play as bosses or have two players as the same character. That was the first version ported to SNES, btw, and I think it was harder than the later versions.
Sega was more known for sports games too.
Re music, I doubt everyone agreed at the time that SNES had better music. Sega definitely had it's own style of music. It sounds more dated now though.
Re both blood in Mortal Combat and 1994 being a big year for SNES, in '94 Mortal Combat II came out on SNES, and that had blood. Didn't all the Sega fighting games have weird controls because it only had 3 normal buttons? That probably gave the SNES port an advantage.
I don't like the MC franchise much but the second game was okay. The SNES version of the original, blood aside, is almost unplayable. Anyone who said they liked that one better than any of the SNES versions of SFII is lying.