UAB is a good choice for anything related to the medical field, plus some of the pure sciences. I believe they have a pretty good EE program, but don't know much about any of their other engineering majors.
Alabama, on the other hand, has a great business school, a good fine arts program, and a well-respected college of engineering.
I personally prefer the campus at UA to UAB, and the town of Tuscaloosa to Birmingham. It's fun to be able to go out at night and walk around the quad and smoke a cigar, or go out there on Saturdays and chuck a football or frisbee with some friends. And I liked being able to wake up a half-hour before classes and still make it on time, and I lived pretty far from campus.
Night-life wise, it really depends on your style of bar, although Tuscaloosa DEFINITELY has more per capita. If you love the college/sports bar atmosphere, Tuscaloosa is the place to go. If you like the occaisional piano/martini yuppie bar, then there are none (to my knowledge) in T-Town. Of course, the two are a reasonable drive away from each other, so when we wanted that type of bar we'd just drive to B'ham and stay with a friend.
Basically, unless your major is in something that UAB clearly outperforms Bama in, or unless you are really accustomed to the amenities of large-city life, I'd go with Tuscaloosa.