Not to sound like a salesman, but I recently picked up a copy of Ajax Security (http://www.amazon.com/Ajax-Security-Billy-Hoffman/dp/0321491939/ref=sr_1_1?ie=UTF8&s=books&qid=1278874728&sr=8-1) and it had a good one chapter explanation and comparison of various Ajax libraries and frameworks in terms of not only security but also speed. If you don't find your answer, I would recommend that book.
I personally would use jQuery because you have a finer control over what is actually loaded. The Update Panel, as I understand, updates all of its contents. You can't pick and choose what is updated inside it, whereas with jQuery, you have absolute control.
As for degrading gracefully: The only reason I can think of why the Update Panel or jQuery AJAX wouldn't work (assuming the server is configured correctly and there are no errors in the JS) is that the browser doesn't support Ajax. If this is the case, neither methods will work. So, I wouldn't worry about the differences between the two in that regard.