It is recognized by Microsoft, that there is some overlap between the two products. However, they do have a different focus:
If you are building a web site that consumes JSON from your web service then MVC is probably the best choice.
If you are building an API intended to be consumed by a variety of third party clients then WCF Web API is the best choice.
My own personal reasons include the fact that with WCF Web API means I can self-host in a Windows service, and I can avoid ASP.NET, web.config and Cassini :-)
