I'm at LSU-NO now, having applied only there during undergrad. There are certainly negatives, but I think the positives far outweigh them, and I'm currently intending to go into academics in at least some form (pedigree matters more).
Cons: Lower prestige nationwide. Not tremendous amount of research $$$ coming in. Charity OOC.
Pros: Med school pedigree is pretty far down the list of things residency program directors look at. LSU residencies love their own. The price is wayyyyyyy lower than you'd be paying elsewhere (unless you're getting $$$ elsewhere). New hospital going up. Home.
Teachers have been really great by and large so far (at new orleans) fwiw. Still sucks (a lot), and I think I may have learned better with systems-based, but still happy with my decision.
If you're not positive where you want to go though, apply a few places. If you're already a med student (your SDN status) there... Don't drop and apply elsewhere...