I think the art is important.
And by that I mean that I can tolerate bad art if it still tells the story, but usually if the art is bad the visual storytelling is bad too. Sometimes I can't even understand what the hell is going on the page, it's like reading a book written in l33t speak. I don't wanna hurt my brain and eyes decrypting the story, so I drop comics like that.
About the art-styles, I won't read the style I dislike. Even if the story is good, I will keep nitpicking its faults just because the art is irritating. So if the art-style changes suddenly into something of not my taste I might drop the comic.
Also, what is the good art? For me, it's something I like of course. Some of the art can be highly realistical and well-rendered, some of the art I liked can be cartoony, but charming this way or another. There's actually no right answer, and every person decides to themselves what is good and what is bad. Of course, there are overall rules of goodness, but as lunox99 said, if the style is "dead" it doesn't matter if it's "well-drawn".
Though, as many people said already, if the story is bad, I will drop it too, no matter of the art style.