I try not to think about it in terms of total compensation, but of marginal income (net income - cost of living).
My taxes here are lower, and my cost of living is much lower. I own a 5-bedroom home on half an acre that I paid $125k for. My mortgage is $850 / month. My entire monthly expenditures, including food and such, are around $3,500.
That doesn't surprise me, but it doesn't change my point. Your math is just slightly different.
I'm not super familiar with NOLA housing prices and such, but I can't imagine that it's on par with SF or LA. That means you can work for a lower base comp and still have the same amount (or more!) left over after meeting your basic needs.
I can't speak for your particular situation.
As someone laid off about a year ago, the answer for myself is supply and demand. I had been holding out for my previous TC, but now I'm pursuing lower-paying positions.
It's disappointing, but I don't take offense at it.