WCF vs ASP .Net Web API
First, I suggest you read my post on the subject: http://blogs.microsoft.co.il/blogs/idof/archive/2012/03/05/wcf-or-asp-net-web-apis-my-two-cents-on-the-subject.aspx
Regarding your WSDL question - since the WebApi does not use SOAP, it does not require a WSDL, and does not export one. You can use Hypermedia to return resources with a list of possible activity URLs (think of it as a self-describing resource)
The choice depends on what we want to do.
- ASP.NET Web API is a framework for building non-SOAP based services over HTTP only - so there aren't more transport protocols available using this framework.
- WCF / Windows Communication Foundation is a framework for exchanging SOAP-based messages - here we use a lot of transport protocols: HTTP, TCP, Named pipes, MSMQ, etc...
I am not sure about which one has better performance regarding the amount of data, maybe WCF since we can use low protocols. Any comments are appreciated.
The WCF Web API primarily focuses on REST implementations. If you are setting up a REST implementation, the standard WCF bits are a bit of a pain in the rear. If you are setting up RESTful services, you will find the WCF Web API a much nicer experience. If you are setting up SOAP services, then the WCF Web API is not your best friend, and you are better off using WCF for your services.