Which one is better to use in ASP.NET MVC?
Instead of making a recommendation I suggest you read Dave Ward's blog Encosia that has a series of posts on MS Ajax/ Update Panel vs. jQuery post mechanism. Dave maintains that the performance of jQuery is vastly superior as it cuts out approximately 100K from the transmission to and from the server.
First of all, it could be useful to take in mind that ASP.NET MVC doesn't support, or better, doesn't has the postback concept..
It's still possible to use asp.net server controls in asp.net mvc, asp.net ajax it's one of them, but asp.net mvc it's made, it was thought, to separate concerns (views) and to be REST styled as close as possible, so taking this in mind the final thought would be:
Sorry for my english
JQuery is purely client side library. Asp.Net Ajax includes both client side and server side functionalities. IMHO, comparison ain't really fair. They might complement each other going by Microsoft's plans.
Personally I prefer jQuery for the following reasons:-
In terms of what MS AJAX offers you in MVC, it can do a lot for you in terms of giving you a quick way to "AJAXify" forms and links, but as far as I'm concerned adding 90kb worth of javascript to do that isn't really worth it when the equivalent calls in jQuery (e.g $.get, $.post, $(element).load) are relatively easy to use.