I've lived in both cities. Denver very recently and New Orleans 20 years ago while in school at Tulane.
New Orleans- Unique, no place like it, some aspects of living there extremely frustrating (very slow, lots of poverty, poor city services). Lots of violent crime. Economy based on tourism and energy and not (currently) as thriving as Denver's. Hot and humid. Did I mention how unique it is, though? Been there recently and a lot has changed....but a lot has not.
Denver- great city. Perfectly sized and offers everything you need. Lots of transplants from elsewhere, and friendly on a superficial level, but a bit insular with people not as overtly friendly as the South. Great neighborhoods with lots of walkability. Active, healthy population. A four season climate with winters not that bad at all compared to the NE or Midwest.
At your stage of life, I would choose Denver, hands down.
Edit: Didn't realize the OP was old. I hope you are liking Denver