Saint Louis Univeristy has about 150 seats in its first year medical school class. However, that number is somewhat misleading. A little less than one-third of those are taken up by their med scholars, that is, undergrads who are pre-accepted to the medical school following they maintain an exceptional academic standard and other guidelines upon graduation. So the actual number of seats is closer to 100. In terms of competitiveness, it's the 8th oldest med school in the nation so it's been around for awhile and thus its reputation is quite solid. The residency match list is exceptional for a school that doesn't rank in the US News top 50 for primary care/research though they are known for producing great clinical physicians as I'm sure other schools are too. If statistics matter, than SLU's hospital ranks in the top 50 of 13 specialties, and was in the top 10 for geriatrics according to US News.
There are many different religions held by the students there and at other Jesuit med schools. It doesn't hurt ones chances for admission. I'm sure if its a major factor in your life, go ahead and mention it...it can't hurt. Just be yourself. As far as other non-Catholic religious medical schools (Loma Linda, Albert Einstein...etc), I'm not sure if it helps to be the same demination.
Hope that helps!
Wyldstyle2000