jQuery
The junk drawer of javascript programming. They got everything you need in there, if you're willing to dig, use some duct tape and super glue, and in general have a group of developers able and willing to hammer code. jQuery is great!
It's used in way more places than you think. However, like Drupal and other community-supported frameworks/libraries, when you get free support, you get what you pay for. You can get it all done with jQuery, but sometimes you need a shovel, flashlight and perseverance.
Additionally, very good documentation (on par with PHP's online docs), and tons, literally tons, of example code and blog entries out there.
Will appeal to tinkerers and "advanced scripters" who are not shy to Google a phrase to find an example that can be used to scaffold a problem and speed development.
ExtJS
Professionally developed by a for-profit company, these are more akin to controls (in the context of Visual Studios) than widgets or plugins. Intentionally complete and robust, with an eye for detail and a higher-level organizational structure than I think exists in the wilds of jQuery, ExtJS is a get what you pay for: A professionally-developed and supported product that lives and dies by it's ability to return value.
Will appeal to professionally-trained "programmers" expecting extensive testing and a higher-order or rigorousness in the development of the controls.