Hello!
I prefer automated testing. When we develop a REST API, the testing is done using the automated testing frameworks of that particular language. Recently, we've used ExpressJS and Play!, both of which are easy to test using associated tools. The thinking is this: if you have a defined API, then your tests on the client and server should be independent, working off the same definition. I don't think there's any reason to consider AngularJS in your REST API testing at all.
For client-side testing, I prefer Testacular as it works very well with AngularJS. Angular contains a special module (`ngMockE2E`) that allows us to completely mock up expected responses from our REST API for automated, independent testing.
Josh