Having used both, Twitter's Bootstrap is a superior technology set. Here are some differences,
- Widgets: jQuery UI wins here. The date widget it provides is immensely useful, and Twitter Bootstrap provides nothing of the sort.
- Scaffolding: Bootstrap wins here. Twitter's grid both fluid and fixed are top notch. jQuery UI doesn't even provide this direction leaving page layout up to the end user.
- Out of the box professionalism: Bootstrap using CSS3 is leagues ahead, jQuery UI looks dated by comparison.
- Icons: I'll go tie on this one. Bootstrap has nicer icons imho than jQuery UI, but I don't like the terms one bit, Glyphicons Halflings are normally not available for free, but an arrangement between Bootstrap and the Glyphicons creators have made this possible at no cost to you as developers. As a thank you, we ask you to include an optional link back to Glyphicons whenever practical.
- Images & Thumbnails: goes to Bootstrap, jQuery UI doesn't even help here.
Other notes,
- It's important to understand how these two technologies compete in the spheres too. There is a lot of overlap, but if you want simple scaffolding and fixed/fluid creation Bootstrap isn't another technology, it's the best technology. If you want any single widget, jQuery UI probably isn't even in the top three. Today, jQuery UI is mainly just a toy for consistency and proof of concept for a client-side widget creation using a unified framework.