The right answer is probably: It depends.
If you're already familiar with one of the technologies, then maybe you should use that one, but I'd rather use ASP.NET MVC.
I am now going to mention two articles by Omar Al Zabir
If you want to go down the ASP.NET MVC route then read this: http://www.codeproject.com/Articles/233572/Build-truly-RESTful-API-and-website-using-same-ASP
If you're going to use WCF then read this about improving scalability: http://www.codeproject.com/Articles/234085/Fixing-WCF-to-build-highly-scalable-async-REST-API
The cool thing about using MVC is that you can write a RESTful app and expose a RESTful API all with the same code.
EDIT: Just to clarify, the MVC RESTful project DOES support GET, PUT, POST, DELETE, so it really is truly RESTful. See the documentation here: http://code.msdn.microsoft.com/Build-truly-RESTful-API-194a6253
specifically this bit:
All these URLs support GET, POST, PUT, DELETE. Users can browse to
these URLs and get html page rendered. Client apps can make AJAX calls
to these URLs to perform CRUD on these. Thus making a truly RESTful
API and website.