WCF
To enable other HTTP verbs you have to do some configuration in IIS to accept request of that particular verb on .svc files
Passing data through parameters using a WebGet needs configuration. The UriTemplate must be specified.
It support XML, JSON and ATOM data format.
WEB API
Unlike WCF Rest service, it use the full feature of HTTP (like URIs, request/response headers, caching, versioning, various content formats)
It also supports the MVC features such as routing, controllers, action results, filter, model binders, IOC container or dependency injection, unit testing that makes it more simple and robust.
It can be hosted with in the application or on IIS.
It is light weight architecture and good for devices which have limited bandwidth like smart phones.
Responses are formatted by Web API’s MediaTypeFormatter into JSON, XML or whatever format you want to add as a MediaTypeFormatter.