I use iBooks and the Kindle app a lot. The interface they present is just better for reading books. I can also highlight a word and look it up or see a mention of a book and quickly check it out on a website, so there’s no loss of interactivity for me. I much prefer WeatherBug to websites because of response time. Maps is also indispensable, and I think more reliable than a Web App would be. Now Playing also has a superior interface. It’s basically a mashup of a Google Maps search for nearby theaters with Rotten Tomatoes ratings. Netflix is indispensable, of course.
As for Web apps I use instead of local apps: FlightStats, Google Voice, and Google Reader. Google Voice is only available as a Web App and isn’t really a content app, but the other two I’ve chosen because I think they have a superior interface compared with the other options I tried.
Most of the rest of the apps I use frequently are utilities, toys and games.
These facts about my App use corroborate Fred’s observations. It’s about the UX! However you can achieve a superior UX, do it, but remember that you must beat the web. This is harder to do on the more comfortable screen of the iPad. On the iPhone, it’s easy, because the screen is cramped.