Im on the jquery evangelism team as well as a speaker at the upcoming Extjs conference. We use ExtJS extensively at Marketo.
If your requirements are simple, publically accessible, and being done by web developers, then use jQuery.
If this is a more complex situation, you have more hard core engineers, behind a username/password, then I suggest ExtJS.
ExtJS is a lifesaver for our flagship product and we clearly fall into the latter camp. However, for our public website, We use jQuery because its more lightweight and easier.
- Here's an overview of the widgets: http://www.bbc.co.uk/glow/docs/1.7/api/glow.widgets.shtml
- This is an overview of the standards support the BBC requires in all its web software: http://www.bbc.co.uk/guidelines/futuremedia/technical/browser_support.shtml
From a UX design perspective, you are never going to beat something that has been designed for your users' specific needs.
Because of that, if you really had to pick between jQuery UI and ExtJS, I'd go with jQuery, since it is more about providing the basic skeleton that you need. ExtJS is over-designed.
I think both have what you need. Try both of them for a while and see which works better for you and by using which framework you feel better!
ExtJS has more controls built in it but jQuery UI core is a little child and you should extend it by plugins ( plenty of them around internet!! ).
But I prefer jQueryUI, it is simple and light weight.