I don't know about open source in general, but GPL'd software is in conflict with the Apple license. If you yourself are the copyright holder, then I (not being a lawyer) would imagine you would be free to license your software under both the GPL and Apple's iOS license, but you couldn't take someone else's GPL'd software and publish it on iOS, without their permission.
Which is one of the points of the GPL, so no big surprise.
I went with MIT + a single condition saying no final work could compete directly with my app. I'm not very experienced with open source licensing. Any recommendations?
I'd say MIT for the code, and license the graphics, sound, etc, assets under a separate noncommercial license. This'll let people peek under the hood, learn from it, and use it in their own app with fewer legal questions as far as what's allowed and disallowed.
MIT vs BSD makes no practical difference. However, the license you have now is not actually MIT, but MIT+your extra restriction. That makes it not open source and a liability for anyone that would use it, since your extra restriction could be interpreted in any number of ways.
One way to keep the option of legal offense against clones is with differently-licensed assets. MIT your code, but choose one of the non-commercial or share-alike Creative Commons licenses. There are lots of them and you're bound to find one that fits your purposes.
Which is one of the points of the GPL, so no big surprise.