I have jQuery UI working on my site OK, and am using tabs fine. I think I did it the hard (wrong) way because I created Squiz assets for all the associated files (bitmaps etc) that it needs and had to get everything patched up so the paths to find everything worked as it expected. I've since been told that if I knew how to play around with Apache config files I could dump all the jQuery stuff in real folders on my server and have them served up outside Squiz but still within the same root URL. I haven't changed it yet but I will when I get a chance and I'm sure it will make getting other external libraries working much easier too.
Also on my site there are some bespoke tabs knocked up with hand crafted CSS and a few bits of javascript or (non-UI) jQuery. That was done by the guys who first built it. Having worked with both approaches I would say the jQuery UI stuff is easier to understand, but perhaps harder to re-style to look exactly how you want unless you're way better at CSS than I am.
Good luck.