I have on several projects.
The biggest difference in my opinion
jQuery UI is fallback safe, it works correctly and looks good in old browsers, where Bootstrap is based on CSS3 which basically means GREAT in new browsers, not so great in old
Update frequency: Bootstrap is getting some great big updates with awesome new features, but sadly they might break previous code, so you can't just install bootstrap and update when there is a new major release, it basically requires a lot of new coding
jQuery UI is based on good html structure with transformations from JavaScript, while Bootstrap is based on visually and customizable inline structure. (calling a widget in JQUERY UI, defining it in Bootstrap)
So what to choose?
That always depends on the type of project you are working on. Is cool and fast looking widgets better, or are your users often using old browsers?
I always end up using both, so I can use the best of both worlds.
Here are the links to both frameworks, if you decide to use them.
- jQuery UI
- Bootstrap