It is also based on SOAP and return data in XML form.
It is the evolution of the web service(ASMX) and support various protocols like TCP, HTTP, HTTPS, Named Pipes, MSMQ.
The main issue with WCF is, its tedious and extensive configuration.
It is not open source but can be consumed by any client that understands xml.
It can be hosted with in the applicaion or on IIS or using window service.
This is the new framework for building HTTP services with easy and simple way.
Web API is open source an ideal platform for building REST-ful services over the .NET Framework.
Unlike WCF Rest service, it use the full featues 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.