Coinbase is already unsatisfying, as far as software wallets go, because you have to register with an email address. Your coins are held in a shared wallet, not on the device. But at least you get the idea of how Bitcoin works on a phone.
On the other hand, Apple didn't explicitly design iOS to be a highly secure environment suitable to store digital money on. A couple months ago, a bug in Android's random number generator was discovered that compromised all key pairs which used it. Android wallets had to issue an update which moved all the bitcoin in each wallet to a new address, generated with the patched RNG. But for a day or two, most Android wallets were vulnerable.