Should I build a REST backend for GWT application
Ask yourself the question: "Will I need to reuse the server-side interface with a non-GWT front-end?"
If the answer is "no, I'll just have a GWT client": You can use GWT-RPC, and take advantage of the fact that you can use your Java objects both on the server and the client-side. This can also make the communication a bit more efficient, at least when used with <inherits name="com.google.gwt.user.RemoteServiceObfuscateTypeNames" />, which shortens the type names to small numeric values. You'll also get the advantage of better error handling (using Exceptions), type safety, etc.
If the answer is "yes, I'll make my service accessible for multiple kinds of front-ends": You can use REST with JSON (or XML), which can also be understood by non-GWT clients. In addition to switching clients, this would also allow you to switch to a different server implementation (maybe non-Java) in the future more easily. The disadvantage is, that you'll probably have to write wrappers (JavaScript Overlay Types) or transformation code on the GWT client side to build nice Java objects from the JSON objects. You'll have to be especially careful when you deploy a new version of the service, which brings us back to the lack of type safety.
The third option of course would be to build both. I'd choose this option, if the public REST interface should be different from the GWT-RPC interface anyway - maybe providing just a subset of easy to use services.
We ran into the same issue when we created the Spiffy UI Framework. We chose REST and I would never go back. I'd even say GWT-RPC is a GWT Anti-pattern.
REST is a good idea even if you never intend to expose your REST endpoints. Creating a REST API will make your UI faster, your API better, and your entire application more maintainable.