I have to assume you mean that you are going to work in New Orleans since you mentioned Tulane and Oschner.
Tulane is a large teaching hospital. The pay is good, one of the highest but the nurse to patient ratio is high. Right now they are offering a $5,000.00 sign on bonus for Med Surg and down from there for other areas.
I do not know a lot about Oschner, you could look on their web site, but they are the premier hospital as far as benefits and work satisfaction. The pay is not as high as other hospitals.
There is also University which is paying high right now, but again like Tulane, this is becoming a charity hospital. There is Touro, a private hospital that pays well and Oschner/Baptist.
Good Luck, I will have some more info for you next week or later this week, because we are doing a study to find out what each hospital in the city is offering.