Security could become a big factor in web vs native. For example, I don't trust the facebook native app. I've used both the web and native versions and the native version is smoother and better. But I don't trust facebook. There's a lot of personal information on mobile phones these days and I don't want facebook accessing that data. For me, using the web version is much safer.

And random apps on the app store from unknown developers? I trust those even less. I may install one if the list of permissions is very restricted and reasonable. But I don't like spending time looking at the permissions and trying to figure out if it's ok.

Another example is banking apps. I remember there was news a while ago that many banking apps were not handling passwords properly. If I use the web, I can see the SSL lock icon, inspect the certificate, and know that it's properly handled. I can't do that for a native app.