the
Rushing Beat trilogy can't get enough love. Rival Turf was the first game we bought for our SNES because we loved Final Fight but wanted to play co op (which wasn't in the SNES version

). Someone recommended Rival Turf and we were hooked.
I didn't even know about
Brawl Brothers until recently, but I strongly recommend checking that bad boy out before moving on to
The Peace Keepers, which is the pinnacle of the series. The branching paths kick much ass, but the US localization is downright horrible. They changed all of the special attacks to lameify them, swapped out the character portraits, and the translation makes zero sense. It's not as bad as Shikigami no Shiro 2's translation, but it's pretty bad.
There's an english patch out for the Japanese SFC rom of it, which I strongly recommend checking out if you end up digging the game.
on a tangent, if you liked
Die Hard Arcade, you may be interested in
Minority Report. For reals. Game was done by Treyarch, who's mostly famous for doing the recent 3d Spiderman games, but they're also the force behind the pc cult classic
Die By The Sword (another one to check out, though it's a bit more of a hack em up than a beat em up

).