Armory offers an easy way to put your coins into cold storage, which is the safest way to store your coins. Unless you can offer that on your iOS app, you can't say you are more secure.
You can always write down your backup phrase and then wipe your wallet from the phone (it forces you to type in your backup phrase in order to wipe, ensuring you didn't make a transcription error).
Also I've read multiple accounts of people who've lost funds with paper wallets because everyone said that's what to use, but they didn't understand how change addresses work. If you have an HD wallet backup phrase instead of a single address paper wallet, that solves that problem. Even experienced bitcoiners have made mistakes leading to loss trying to manage paper wallets.
Paper wallet is most secure though there is some problem such as damages to paper but you can prevent it(most of them doesn't do). Back up phrase are very hard(est) to crack, but still there is a chance, less than 20% maybe. You don't want to really use "change address" feature if you don't know about it. Just use an address, store 90%+ of your BTC there and a small amount in a hot wallet.