For me style is really important. Moreso for professional level works though. Avatar is a great example. I can't get into the aesthetic no matter what, and that's a deal breaker, I'll never watch it.
On amateur stuff...I'm not as harsh. But I do need to be at least minorly interested in the style to check it out. Note that style doesn't mean technical abilities, for me, it means if it causes a gut reaction of interest.
Overall, I don't want to come across as a snob, but, I'm really picky when it comes to what I look at. So the answer is, style definitely sways my interest.