Houston is in the same predicament, depleting the water table and sinking rapidly. The taxpayers will continue to be on the hook for Nawlins, a fools errand, IMHO due to corrupt politics and demographics.
I think Texas is moving forward to try and save Houston, particularly after Harvey.
Both have close proximity to the coast, but that is where the similarity ends.
Houston is not built like New Orleans on a delta system which is composed of sediments that highly subside over time. The mud which discharges from the river that used to build up the delta is now carried via levees into the Gulf which actually benefits Texas with sediments on its western side.
Houston also does not have a large river system running through its center which has to be contained during high river stages.
And Houston is not below sea level like a lot of New Orleans, which means water has to be pumped out.
Houston does of course have the burden of more groundwater removal which causes some subsidence.