The limit we've run into with iOS is not getting a good looking UI. Rather it's the performance of Javascript in Safari. We have a fairly large one page webapp that looks great on iOS however the performance is an order of magnitude slower on an iPad than Chrome on an old laptop.
You can't just take a desktop app and stick it on the phone. It will perform poorly.
But you have to design mobile (web) apps from the ground up relying on the strengths of the mobile platform.
One idea is to limit the functionality of the mobile app. Tasks which are very UI heavy should probably be simplified or removed.