An hmac and a symmetric cipher are not mutually exclusive ideas. In fact AES-CMAC which is both an MAC (not hashed) and a symmetric cipher, AES-CMAC is the cryptographic primitive that makes WPA secure. (Although a WPA can still be broken using a rainbow table).
You should not need an exotic authentication system for this. Logging in with a username and password and maintaining session state with a cookie is commonly used because it is easy to implement and it is secure. By storing state, like a cookie its no longer technically RESTful, but there is nothing stopping you from doing it.
However, in terms of authentication I believe that asymmetric cryptography like RSA is the most secure. (Amazon uses asymmetric cryptography for ssh connections by default.) This allows you to only store the public keys, so that if your server where to be compromised no authentication credentials could be used. It also defends against MITM attacks. In many cases this can be implanted quite easily with REST because HTTPS already supports client certificates. You can sign the clients certificates for free and then verify them your self.
If implemented properly, the strength of an hmac vs symmetric cipher it mostly comes down to the strength of the secret. If you are using a secret like a password, then both systems are equally very weak. These secretes must be large, Cryptographically Secure Psudorandom Numbers. Another thing to keep in mind is that symmetric ciphers are very difficult to implement properly. Most programmers do not understand this and end up reusing PRNG when using stream cipher or when using a block cipher they use an incorrect mode and leave the IV null. By contrast HMACS are very easy to implement and less can go wrong. If everything is transmitted over HTTPS, and your are using an hmac then its easy to implement a secure authentication system. If you really want to implement a symmetric cipher you must get a copy of Piratical Cryptography, there are a few chapters devoted to symmetric ciphers alone because so much can go horribly wrong. You also have to take key distribution into consideration, ssl uses a DH-Key Exchange for its symmetric keys.
Make sure to read the OWASP top 10, especially Broken Authentication and Session Management. This requires the use of https for the entire session, most web application programmers don't realize this.