ASP.Net web api Vs .Net core web api

It is very difficult to answer your question, because fast is relative. But I would say that the ASP.NET Core stack is faster than the old ASP.NET / WebAPI stack.

There are some reason why ASP.NET Core is faster:

• It was build for high performance, scalable (cloud) scenarios
• No dependency to the old System.Web.dll
• Much leaner execution middleware pipeline (Owin)