I might be insane for saying this, but I think I prefer the first one best.

Sure, the graphics are a lot better on this one, featuring some of the finest spritework of its era, and the soundtrack is arguably one of the absolute best of all time, but I find the level design to be a tad boring and very similar to each other. The first one had that fantastic elevator section where you could throw off enemies, the one in the factory where you could use the industrial press to your advantage, and the bridge under construction where you had to watch your step. The addition of special moves is fantastic, but I don't know if the trade-off is worth it. 

Still a fantastic game, Streets of Rage is one of the best (if not the best) beat-em-up franchises of all time.