WCF vs ASP.NET Web API

The choice depends on what we want to do.

1. 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.
2. 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.

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)