I don't have a comprehensive list, but here are a few I've noticed:
- Outlook for iOS routes all email, attachments, and Exchange credentials through Accompli's / Microsoft's servers. TouchDown does a direct connection to Exchange and does not route your data through any third party servers.
- Outlook for iOS cannot synchronize contacts with the device phone book
- Outlook for iOS does not support S/MIME
I haven't tried the Android version yet.