Two of the main reasons are Display Modes and TAP support.
Also, you don't need ASP.NET MVC 4 to use ASP.NET Web API. Just install Microsoft.AspNet.WebApi package into your existing ASP.NET MVC 3 project, you will be good to go. Just be careful for the order of routes. Both ASP.NET MVC and Web API routes collected under the same collection and a request may go into another pipeline rather than intended one if routes aren't set up properly.
Also, you don't need ASP.NET MVC 4 to use ASP.NET Web API. Just install Microsoft.AspNet.WebApi package into your existing ASP.NET MVC 3 project, you will be good to go. Just be careful for the order of routes. Both ASP.NET MVC and Web API routes collected under the same collection and a request may go into another pipeline rather than intended one if routes aren't set up properly.