iOS Open Source
You have the opportunity to see how the app works.
You have the control
If the app doesn't give you the access of the private key(s), you are not the owner of your bitcoins from a technical point of view.
Privacy Advanced Security Misc
HD Key
You can export the key which controls your bitcoins outside of the wallet.
Generally based on BIP32/44.
You have an autonomous wallet which verifies transactions without depending on a central server.
Recovery Phrase
A set of words to backup/recover your wallet.
Generally based on BIP39 and also an HD key.
PIN Protection
PIN or fingerprint protection.
Payment Protocol
Better transaction security between a merchant and a customer.
Based on BIP70/73.
SegWit Ready
Better transaction security.
Lower fees.
H/W Support
Compatibility with hardware wallets, like Trezor or Ledger.
No Registration
You don't have to sign up with an email or personal informations.
Well Designed
The app has a design that approach the guideline of iOS and has a good UX.
5 languages supported, at least, translated by professionals or verified for each language in translation platforms (Crowdin, Transifex...).
Can Buy Bitcoins
With fiat money in the US and EU, at least.
Credit/debit cards are highly preferred.
Coinbase 3680
Concerns Coinbase.

Bitcoin Wallet 458

breadwallet 204

Unverified translations.

4.0 on Apple Store

No update since August 2016
Concerns Xapo.
Europe USA Canada
Airbitz 103

USA Canada
(Based on Copay)
5 on Apple Store
The server side is still open source and can be selected in the app.

Only with the
Copay Chrome App
Europe USA Canada
Coinbase + Glidera
Luno Bitcoin Wallet 31
Concerns Luno.

Mycelium 22
Europe USA Canada
Coinapult + Glidera
Local Trade