jQuery+jQueryUI Vs Yahoo UI..Which is the best UI to use in asp.net web applications?
At the extreme risk of getting downvoted I think your question is a little open-ended to be answered in a single answer.
I think in this case the answer must be there are horses-for-courses. By that I mean you need to choose the right technology to suit the problem you are trying to solve.
You have not provided us with enough information to make a critical judgment on your needs. All you have asked is which is better and the answer is neither. They both fit a need. They overlap in a great many places but each also has it's own unique advantages.
So I guess you need to either provide us with more information on what problem you are trying to solve or gain an in-debth understanding of both technologies to see which best fits your solution. It may be that you need both or you may decide to role your own.
If you have a particular issue then please create a new question with the particulars and perhaps someone will be better placed in giving you an answer.
However, having said all that, I'm a huge fan of jQuery. It's easy to use and lighweight. I can very quickly and easily write my own plugins and there is a great community out there sharing their own plugins.
I can't speak for the Yahoo UI as I haven't used it in quite some time and at the moment when I begin a new project I instantly reach for jQuery. But that's my own personal, and possibly subjective, choice.
Good luck.