Personally, I think it looks awesome, but like ror.mcleish said, this is an extremely subjective matter. I honestly think they did an amazing job at revitalizing a 90s franchise, making it appealing to both existing fans and the new generation of gamers. My girlfriend is 25, she had never played (or even seen) a Streets of Rage game, and she immediately fell in love with the art style, the animations, the attention to detail and just how colorful the game is. Me, having grown up mostly as a Nintendo kid, I only got to enjoy the Streets of Rage games whenever I visited my cousins or went to friends' houses and they owned a Mega Drive (which was pretty much every other kid), but I feel they kept it pretty close to what I remember -- come on, those were 16bit games, they looked very cartoony, anyway.
If you dislike the art direction, that's your prerogative, the studio is not going to change it, so... yeah. Sorry, I guess...? Despite all of that, the game IS a very solid brawler, so there might be something in it for you and others who dislike the art. Seriously, it's an extremely well-made game, technically sound, fluid, just... fun to play.