That all depends on what you mean by "better". It depends on what you want for your birth experience. If you would like the nurses and docs to tell you what to do and be a passive patient, then any hospital is "good". Baptist downtown has the most advanced NICU so if you are high risk, you might consider that the best.
Many of the hospitals still separate mothers and babies, which is bad practice in my opinion. St. Luke's is better than the rest when you consider this. You won't have to fight them to hold your baby and keep your baby with you (where it belongs).
That being said, if you are considering an unmedicated birth, Baptist downtown is probably the worst. St. Vincent's would be 2nd worst, followed closely by Memorial (hmm, maybe that's a tie). In my experience, the nurses prefer if you stay in bed, let them do their jobs, get an epidural, and be an "easy patient".
St. Luke's is the best if you would like support in what is sadly considered "alternative" birth choices. 3 of the nurses there have actually had out of hospital births and they are better at supporting moms who are educated about their options and know that they have a choice in how their care is handled.
I suggest finding a childbirth class that is NOT sponsered by one of the hospitals, so you can get some non-biased information and consider all of your options.
Better yet, take a tour of the local birth center to see the best place in town that normal birth is supported. check it out at www.fruitfulvine.com
Best of luck to you