While I don't usually spend a lot of time, discussing the different ports of games, Final Fight is clearly a case where the experience can differ extremely depending on the platform.
The initial port for the SNES looks good but is missing many features and censors certain aspects that were too risque for Nintendo of America. This version is really only of interest for collectors of that console and, otherwise, should be avoided. Each of the other ports, though, have unique selling points. While it is not arcade perfect in terms of visuals,
the Sega CD version restored all of the missing content from the SNES version, and it remains of interest today for its high quality CD soundtrack, which has not been featured in any other ports. The GBA port, called
Final Fight One, likewise has unique cut scenes and other bonus content not featured in other ports that help it to maintain relevance, but the performance and aesthetics are not arcade perfect. The best official ways to play the game, then, come in several of Capcom's arcade collections, which emulate the original hardware.
Capcom Beat 'Em Up Bundle is a bit bare bones but includes a faithful port and is the best way to play on current gen hardware.
Capcom Classics Collection, on the other hand, is older but features a better set of options and remains a very good port today. Still, the best version is arguably
Final Fight: Double Impact, which boasts the best set of features, including achievements, the most robust set of visual options, and an optional remastered soundtrack (albeit one that is inferior to the Sega CD soundtrack). The downside with
Impact is that only one other title is included, so it's certainly less of a bargain than the other titles. Despite that, it's still the best way other than the original arcade board to play
Final Fight, but any of these collections will deliver, so you should simply pick-up whichever is easiest for you to play.
Disagree with the consensus here. This is a stone cold classic and it's mindblowing how much they got right in 1989 already. This game is what set the bar and is unarguably the most innovative beatemup EVER made, and very few beatemups really manage to reach the same heights, despite copying so many mechanics and qualities from FF.