I'll be starting at Tulane this year, so I thought I'd share my experiences from applying last cycle. From what I saw, MCAT is much more important than grades. The average stats for last year's entering class were 33.3 MCAT and 3.4 cGPA. That's an exceptionally low GPA for a school without strong instate preference. When I was at the interview one of the adcoms said that their average MCAT scores have been steadily increasing, so it might be up another point or so for this year.
A big part of the reason their cGPA is so low is that Tulane frickking loves nontrads! I'm 30 and half my interviewing group was just as old as I am. If you got bad grades in undergrad but performed well in a postbac, chances are good that adcoms will look beyond your cGPA and judge you by your recent work. Tulane doesn't give out many interview invites, so a majority of interviewed candidates get acceptances. I suspect that this means they also place a heavy emphasis on ECs, since they're trying to only interview people with the personalities to become good doctors rather than sort out the good from the bad at interview day.
Since someone will ask for my stats if I don't share them here, I've got a 3.15 cGPA and 32P MCAT. I graduated back in 2004 with a 2.89 GPA and a transcript riddled with Ds and Fs. Last year I went back to college and got a 4.0 in a self-constructed postbac. I've done three years of full time volunteer work, mostly overseas. I think I applied to 20 schools, half MD and half DO. I got an interview invite at my state MD school, but Tulane ended up being my only MD acceptance. I'm very excited to start there, and I will always be grateful to Tulane for recognizing that my awful grades in undergrad are in no way indicative of my potential performance in med school.