RSS feed just plain sucks now, so I'm not even going to compare it
I'd say using the app brings the most cohesive experience to AC, BUT, there are still two very important advantages that, so far, only the website offers that keep me coming back to AC on the web:
1) Device-independent. If you install the app, you can only use it where you installed it, and we all know iDevices keep rejecting any Android-related apps, including news sites. My computer also doesn't have an AC app available, so I just keep firing up the web browser instead of going to my phone to check on AC news.
2) This was a recent addition to the site, but a very welcome one: Notifications to replies. If you comment on a story, you can select the option to have an e-mail notify you whenever someone replies to your comment. That option is currently NOT present in the AC app.