"New" Marigny is not a term I've heard. But I do know the Marigny, as it was the place where I had my first apartment after moving here 20 years ago.
Before Katrina, there WERE safety issues in that area. However, the crime was related to neighborhoods adjoining the Marigny, which were slums--no way to sweeten up that fact. Since Katrina, everything is different. Neighborhoods I wouldn't have felt safe driving through in the past are revitalizing. The Times Picayune [nola.com] has a lot of archival material regarding the flood and Katrina. The paper also lists crime stats. I would start my research there. Another way is to simply ask neighbors in the area. Drop a note in some mailboxes and leave your email address. New Orleanians are the best people. You'll get good, honest responses. If an area is gentrifying, it is in the best interest of the homeowners there to have houses on their block sold as residences. The tighter a community is, the safer it is.