A Guide to Designing and Building RESTful Web Services with WCF 3.5, this article explains the foundations of REST and how it relates to WCF. MVC uses REST as the architectural model. I am guessing one can use the .NET MVC to create web applications that have both a front end and an API point, but I am not sure if the safe way of building the API is to build it with WCF and then use it in the MVC as a controller.
Please comment if the question is not clear, I will add or modify the text.
Theres actually a third option, ADO.NET Data Servies. Anyway, here how I see them.
MVC REST: Gives you full control over how to expose your data, you have to write all the code to get it up an running tho, e.g. serialization, deserialization, all the CRUD methods etc etc. Worht metioning that this being an MVC site means you are limited to exposing your service via IIS over HTTP(S)
WCF REST: More automation than MVC, a much more solid frameowkr than MVC REST, i.e. caching, security, error handling etc (basically all the stff you’d have to write yourself using plain MVC). Being WCF, you can host this in a variety of ways (e.g WS-, TCP) etc.
ADO.NET DATA SERVICES: The quickest way to get up an running with everthing ready to use, all you need todo is configure the global.asax, however you have to use an Entity Data Model, which you many not want to.
Personally, I would use either ADO.NET DATA SERVICES or WCF REST to build an API, consue that API in MVC site and then expose that API either directly, or by passing it through another layer.