I would really like to hear more, especially from people who attended med school or residency in NOLA or Louisiana in general!!!! Those from the state know way more than any out-of-state folk. The good and bad.
I went to medical school in NO, but I'm not a categorical, so my opinion is based on rotations at University Hospital, Touro, and Ochsner campuses as a student and a prelim. From most of the IM residents I've spoken with (the ones who looked into all the NO programs closely), LSU Baton Rouge is seen by most as the top program in LA. I can tell you first hand that the BR rotation is the top choice for the LSU medical student rotations. There have some BRILLIANT residents who chose to go to BR over some elite programs out there. George Karam, the PD in BR, is probably the best faculty member on staff at LSU (including NO); and he has a collection of annual awards to prove it. It's tough to explain,cut he just has a "wow" factor about him. His lectures are very captivating as well as motivational (a healthy blend of personal experience into his topics); and he has a way to make things stick on the first time go round. I can't say how the move from Earl K Long to Our Lady of the Lake (which started midway through last year) has affected the program; but I'd highly recommend looking into it. Baton Rouge is also a very fun city and only an hour outside of NO.
LSU NO is in a bit of a transition process right now, though they are currently building a state of the art University and VA hospital that is supposed to open in 2-3 years. I can tell you that they have some excellent faculty, and the population of patients the hospital gives great exposure in all specialties of medicine, ID especially with the large population of AIDS, TB, histo, blasto, etc. I feel they did a great job of balancing academics with clinical learning, and I can tell you that the LSU students who trained under their staff tend to get high marks when rotating outside the state. The fact that they didn't match a few slots last year was more a result of political budget cuts, though I can't comment as to how things have changed this year. It's worth looking in to.
Ochsner Medical Center is another program in NO. It's without a doubt the best hospital in the state, though they don't quite have the academic reputation given they're not associated with a US medical school. Their clinical experience is outstanding, though. Their fellowships seem to be a big draw to the program for the categoricals, as the hospital is nationally ranked in cardiology, GI, endocrinology, And pulm ontology. Residents stay very busy while working reasonable hours and get exposed to both private patients and the indigenous population of NO. Staff is very friendly, and the transitional navigators and pharmacologists make it very easy to focus time on patient care and not the hustle and bustle of dealing with placement and follow-ups (something that LSU NO didn't have at the time).
I don't have much inside info on Tulane's program as far as academics are concerned. I worked with some of the residents during a VA rotation, and the few of them all seemed down to Earth and happy with their choice. The Tulane name definitely carries more weight in national academics than LSU and Ochsner, which will likely look better on paper when it comes time for fellowship applications, but I don't know how their match lists compare to the other programs. From an in state perspective/reputation, though, there's not much of a difference between the Tulane and LSU training/medical school. I would also like to dispel the notion that Tulane residents get more respect in the hospital than LSU residents. That's laughable. If anything, their students have garnered the reputation as being somewhat lazy on the floor. I know many former Tulane students who own up to their med school stereotype, and I've definitely seen that kind of attitude coming from them on the floor. The residents I currently work with who went to medical school at Tulane, though, are good physicians with good work ethic. As far as their IM residents go, I've never come across a personal issue, so you can take my personal experience and leave it at that. Again, you asked from an insiders perspective, so I'll say what I know. I've heard several complaints from residents and faculty (as a medical student and intern) about the Tulane residents being somewhat difficult to work with in terms of the LSU/Tulane and Ochsner/Tulane cross coverage. To be fair, it's not specific to their IM residents, and I've also never heard the complaints from the Tulane side of things (two sides to every story).
I honestly can't give any info on LSU-Shreveport. It's not a place that many people from New Orleans like to end up, if only for location.
Anyways, I hope this helps somewhat, despite a lack of details about the programs. Again, I'm not a categorical, and I'm not staying in LA for residency, so I really don't have a dog in this race. I just feel like most of the info out there regarding the programs are from people not from Louisiana and is based more on name value than actual experience. Best of luck to all of you.