Will there be an ajax request to update some block using Ajax.ActionLink and RenerPartialView on the one hand faster than using asp: UpdatePanel on the other?
Yes, it will be faster because it sends less information over the wire. You also have full control over what is sent over the cable, and can optimize it.
WebPorms UpdatePanel, on the other hand, sends all view state, making requests more voluminous, leaving you with very little control. This also has another drawback: it relies on the Microsoft javascrpt library, which is probably the biggest library error they created. It's good that they did not approve of it in favor of jQuery, starting with ASP.NET MVC 3. That's why you are more and more people using jQuery even inside their classic WebForms applications to work with AJAX files instead of relying on UpdatePanel.
But the underlying technology is exactly the same: the web browser is an XMLHttpRequest object.