ExtJS can actually be used with jQuery. Since it's a widget library, they've chosen to be DOM library agnostic. It currently supports their own base, jQuery, YUI, and prototype.js. They talk a bit about how to use the different bases here: http://www.extjs.com/blog/2007/08/01/ext-v11-released/, but that post is really old. It may have changed in the time since, I don't know.
AFAIK, you can use jQuery as an ExtJS adapter, instead of the native one. This is only useful if you are adding ExtJS to an existing app that uses jQuery.
