Concept Art House CEO James Zhang (his company has created art for Zynga and the rest of the social gaming biggies) breaks it down further in this Inside Social article where he talks about just how important art is to the success of a particular kind of game. It works out to something like this:
Puzzle Games (Bejeweled): Kind of Important
Resource Management Games (Diner Dash): More important than puzzle games
Text-Based Role-Playing Games (Mafia Wars): 'Extremely Important'
Decoration Management Games (FarmVille, Ravenwood Fair): 'Extremely' important to less important
I agree that you can get away with having less than fabulous art for a puzzle game -- though that makes it hard to compete with the likes of Bejeweled Blitz and Zuma Blitz -- but I have to question how important it is to have high-end production values and art for a game like Mafia Wars. In fact, when Zynga started to incorporate more Flash elements into the game, there was a major outcry on the forums to keep the game text based and avoid the super snazzy visuals.
I'd also argue that games like FarmVille (categorized by Zhang as 'Decoration Management Games'), production values will start to be more important than ever. First, keep in mind the audience in these games -- women -- who tend to be more concerned with decorative aesthetics than men (a generalization, of course), and that these games rely on people buying virtual items to stay afloat -- and the more attractive they are (just like a clothing or shoe store) the more likely they will be purchased.