What's benefit using jQuery Autocomplete over Ajax AutoCompleteExtender? Can some one explains the benefits one over another?
I would vote for the jQuery Autocomplete. Although the MS ajax toolkit still seems to be a live project the Microsoft team have turned their focus to jQuery and producing jQuery plugins of their own. From a personnel point of view developing anything with the control toolkit extenders was a bloated, buggy and generally painful experience especially when you needed to slightly tweak or extend the default behaviour of the controls.
A major benefit is the level of support. The user base for anything jQuery is huge now. If you encounter a bug a patch or workaround will come around much quicker than if you find an issue with an extender - especially on StackOverflow!
The extender would be ok if you had zero javascript experience and needed to drag and drop a widget to roll a prototype quickly but if you have any jQuery experience or none but a little time on your hands it is well worth learning how to use the jQuery Autocomplete version.