That modularity is nice in theory, but Dojo gives me 170kb of compressed javascript simply for selecting the fileuploader widget. I saw the same for Google Closure Library by the way - not saying I could write an all purpose js library which would score better.
That's one of the major things that 1.7 fixes and 1.8 will fix even further... smaller modules and finer-grained dependencies so you aren't pulling in nearly as much base code for each feature.
If what you have to do is manipulate the DOM and do XMLHttpRequests, then jQuery is more than good enough, otherwise Dojo has a lot to offer.
Some features from Dojo which are not about DOM manipulation or XMLHttpRequests that I use a lot:
- AMD-style modules (you can have this with jQuery, but Dojo is built with AMD from the ground up) http://livedocs.dojotoolkit.org/loader/amd
- the build system http://livedocs.dojotoolkit.org/build/index
- object stores http://livedocs.dojotoolkit.org/dojo/index#store-dojo-store
- deferreds (jQuery has these now) http://livedocs.dojotoolkit.org/dojo/Deferred
- templated widget definitions http://livedocs.dojotoolkit.org/dijit/_TemplatedMixin
- publish/subscribe http://livedocs.dojotoolkit.org/dojo/publish
- observable attributes http://livedocs.dojotoolkit.org/dojo/Stateful
This doesn't mean that you should be using it, just use what feels better for you. For some people (like me), Dojo is what feels better.