Neither BCM (Houston) nor BUMC (Dallas) are affiliated with Baylor University (Waco).
BCM is an 'academic' program, although not affiliated with a university (yet... *cough*Rice*cough*); there are more community-based experiences in St Luke's hospital. BUMC is a 'community' program that still has some substantial research opportunities, and is one of the largest single-entity freestanding medical complexes in the US.
BUMC is a pretty cush program. BCM is not.
BCM's program is very large (~150 interns I think). BUMC's is very small (~15 interns I think).
Nationally, fellowship- and prestige-wise, BCM is better-known and will expose you to better opportunities. That said, BUMC is probably one of the more academic private centers, and will in all likelihood give you a decent shot at most competitive fellowships (they have their own cards, GI, renal [soon], and heme/onc fellowships).
BCM is in Houston. BUMC is in Dallas. I guess that's a matter of taste (Although the right choice should be obvious [Houston]).