I care far more about working someplace small than about working on something web-based. There's just a lot less communication and bureaucracy, better odds of avoiding dysfunction.
Web-based startups just happen to satisfy both these constraints - the web as delivery mechanism yields instant feedback, and the web as eco-system encourages small and agile organisms.
 And high quality feedback. As an academic I was separated from my readers by an advisor and a dissertation committe, or by a set of anonymous reviewers and a program committee. Large companies separate you from the customer by layers of hierarchy. In a startup you're right next to your customers.