These two frameworks just aren’t trying to do the same things. They overlap in the functionality they provide, but they are not trying to do the same things
Both are fantastic libraries/frameworks and I think the better question for you to ask is
Which one should I use for this project
This can be determined by circumstances beyond your control e.g. The project leadership has already selected a framework for you, or the application development framework you are developing on is already using one over the other – and you may wish to avoid bloating-up your application with multiple libraries and increasing load times (not to mention script conflicts).
Here’s an example of what the world’s most popular PHP content frameworks have chosen:
Drupal – jQuery
WordPress – jQuery
Joomla – MooTools