Don't try to one-up Apple by doing slightly better versions of what they do, or offering apps they'll inevitably need to add themselves.
Apple always look out for their customers. They will always look to improve the experience. If that means adding software to their platform then so be it. If that software is in direct competition with your software, then so be it. If they roll out the software as a free update across all operating systems, leaving you for dead, then so be it.
Their ball. Their game. Their rules.
Des offers a piece of advice from Joel Spolsky:
A good platform always has opportunities for applications that aren't just gap-fillers. These are the kind of application that the vendor is unlikely ever to consider a core feature, usually because it's vertical â€” it's not something everyone is going to want. There is exactly zero chance that Apple is ever going to add a feature to the iPhone for dentists. Zero.