If you havent tried it give it a try. Its workflow is different and until you get used to it you wont appreciate it.
The reason I keep using Apple Mail is that those competitors for the most part don't offer these features (at least to my knowledge there's not a single competing solution out there that supports all of them):
- non-GMail accounts (Exchange, standard IMAP etc.)
- email encryption
- multiple signatures for multiple accounts
Not sure about encryption, but it's bound to have a PGP plugin or something similar. Postbox is partly derived from Thunderbird, so it would probably satisfy your requirements as well.
Edit: Just realized that I've assumed Apple Mail refers to the Mac version. I'm not sure about iOS, but the new Microsoft Outlook (rebranded Acompli) might do some of those things. Personally I use mobile only for triage, and write emails when I'm on my laptop.