The two programs are very Different.
Baylor College of Medicine is in Houston and is not affiliated with Baylor University the Baptist undergraduate institution (was many years ago, they split up before my lifetime). It is a large (12 person) rigorous program that trains mainly at a county hospital (Ben Taub) and a private hospital (St. Lukes) in the Texas Medical Center.
Baylor University Medical Center in Dallas is affilitated with the religious private school and is a smaller program (5 residents). I don't know as much about this program, but it is my understanding that BUMC is private.
I am from Texas and applying right now, I did not even apply to Baylor in Dallas because I don't want a religiously affiliated program. Most of my classmates that I talked to did not apply either. Also, there are much more research opportunities at BCOM and the hospitals (mainly St. Lukes) are much more highly ranked. If you are are looking for the relatively "well-known" Baylor, it is BCOM in Houston. If you have any specific questions just let me know!
