Double Dragon 2 arcade is pretty bad. The NES version was a marked improvement over the original but in the arcade DD2 is a rehash of DD1 with the same engine, same number of stages (4 as opposed to 9 in the NES game), similar enemies, and a lot of slowdown. Major differences are the aforementioned new control scheme (which made it into the NES version) and Jimmy's cool new white outfit (which didn't). It also has what I feel is one of the saddest endings in a video game, especially if you've played the NES game (not gonna spoiler-tag a 30-year-old game, sorry): In the arcade version the game ends after you fight a ghost version of Billy (and Jimmy in 2-player mode). In the NES game, this was the stage 8 boss fight ("The Double Illusion") and it set the stage for the final confrontation with the Shadow Master. In the arcade version, there is no such fight, and rather than just another challenging sub-boss, it feels like the Lee brothers are fighting their own grief and guilt over not saving Marian. In the NES game, Marian triumphantly rises from the dead after the final boss fight, but in the arcade, nope, she's gone. It ends with a photo, presumably taken shortly before her death, of Billy and Jimmy (with sick mullets) looking creepily at Marian and she blinks and a tear falls from her eye to the bottom of the screen and forms the words "The End." And she's not back in part 3 (the arcade version). As for part 3, it's very different from part 1 and 2: it features much improved graphics (but poor animation), a whole bunch of new playable characters, and a new "store" feature where you buy extra lives and power-ups for real coins. Remember that Technos also made Superstars and Wrestlefest, two similarly money-grubbing games. I said it was different, but it's not particularly better. Again, the NES version is superior, and as Kahran Ramsus mentioned it's the worst received of the series, so look forward to playing the arcade version.
Last note on Double Dragon 2: They released an "arranged" soundtrack in Japan and it included this rendition of the NES version's final boss fight which is pretty goddamn great imo:
https://www.youtube.com/watch?v=RaA7JTa6c-8