Fighting games for me until recently were something that I played completely casually with friends and otherwise ignored so I don't know what the general feelings are but I always really appreciated the Third Strike soundtrack because not only do I personally enjoy the music but you get a really nice variety from things like Kenya to Mexico, New York to Germany, England to something like Ryu's or Akuma's stages. Themes were fitting to a character or to a stage and pulled from different genres which is pretty refreshing, as well as fitting the world tour aspect.
Not that there is anything wrong with having a single motif, Skullgirls is mostly pulling from the same few places for what it's trying to do with music but it fits with the aesthetic as a whole as well as just being outstanding.
For a genre where gameplay really is the most important aspect, more so than any other (aspects, not genres), music does take a pretty high place in my opinion.
I think that nailing an aesthetic in a fighting game doesn't have as much as to do with graphical fidelity as it does with setting a consistent theme and tone made up by art style, musical choices and... I don't know how to put this in a way that is concise without sounding to broad, but the animation itself, not even how technically impressive it is as much as what it conveys, the way characters move needs to say a lot about them as a person, how they fight and how they function.