Which one is better to use in ASP.NET MVC?
First of all, you could use either, as long as when you are talking about Microsoft Ajax, you are only referring to the client library. You can use the MS Ajax client library and most of the toolkit extenders without any server side controls. I have built a pretty big application using web forms and Microsoft Ajax then converted it to MVC/jquery. I found that I was using less and less of the features in the MS Ajax library. There is so much available with plugins, that its making even the ajax toolkit obsolete.
If you are talking about MS Ajax using update panels etc, then I would say no, you can't use them in MVC. In fact, don't use them at all! update panels are simulated ajax, the page still goes through its lifecylce almost defeating the purpose of using ajax.