- Airgapped transactions. Private key is only on offline computer.
- Deterministic wallet. Only one backup, no matter how many addresses you create.
- Ability to bring in my own entropy from a dice and deck of cards (which you can do perfectly well in Armory even though it's not explicitly shown in the UI, as explained in one of my tutorials).
- Encrypted wallet file for backing up to online computer, such that it can be customized to use lots of memory (scrypt) before using a decryption passphrase. Crucial protection against brute-force attacks.
For me, the first two points are a must. In addition n-of-m PAPER backups (shamir secret sharing or similar) is important.
Bring my own entropy is nice to have, but any system that allows paper backups can be tricked to accept your own entropy.