You should always do encryption as a layer outside of authentication.
Authenticate-then-encrypt (AtE) is subject to attacks that encrypt-then-authenticate (EtA) is not. How practical those attacks are depend on exactly what you're using for your encryption, but they can occur surprisingly often, and you don't want to have to worry about them.
The most prevalent class of such attack (in my opinion) is when you've got a (possibly public-key) encryption system that isn't reaction resistant. The encryption might be somewhat homomorphic, in that the adversary can modify the ciphertext in such a way as to make it come out to the same plaintext some of the time, and a different plaintext (or \bottom) some of the time. Then the inner authentication will fail, and the adversary will know which happened. Lattice-based crypto often has this problem, as does McElice (see our 1999 paper on this). Other encryption systems may have this or similar problems, as protecting against this isn't generally something that's a design goal of semantically secure encryption. (If your encryption is IND-CCA2, you're safe, but then you've basically got the authentication built in, anyway.)
Authenticating the ciphertext avoids the whole issue.
Of course, it may have its own issues, if you're using signatures (and not MACs) for authentication, and you want, say, to hide the information of who's signing the message. If you have complex requirements like that, though, you might think twice about designing the crypto protocol yourself.