One of the biggest differences between Baylor and UTH is that Baylor (at least claims) to have a higher emphasis on psychotherapy training. If you're really into therapy, then Baylor might be the place for you. However, less than 15% of all psychiatrists use therapy on all of their patients, and UTH is still required to provide training in it, so it may not be that big of a deal.
The next thing is name recognition. Baylor is the place to go, if you care about that stuff. You would get just as good an education and faculty experience at UTH, though, and name recognition may not matter after residency anyways.
As for the "culture" of UTH, that's really code for one main thing - residency at UTH is less stressful. Baylor residents have a more intensive call schedule. You may say "I welcome hard work and long hours," but does your family welcome not having that time to spend with you? Overall, the residents at both schools were very laid back and friendly, but I did hear more stories of pissed off residents slamming doors at Baylor.
Really, the quality of training is identical at both places, so ignore the hype and figure out the place you fit best. If you want a less stressful residency, got to UTH. If you want a degree from Baylor, and feel that is worth driving 45 mins every day to get to the Menninger Clinic (I think I heard it's moving, but Baylor has halted several building projects because of their potential merger with Rice, so who knows when that might happen) and several more calls, then go to Baylor. Either place has great faculty and residents, so it's up to what you feel is more important to your quality of life.