The people in the nursing home were in "assisted living" and had little opportunity to leave on their own.
The citizens of New Orleans, people served by the mayor, may have been reliant on the mayor for help (his civic duty) but they had to get themselves to any sort of shelter (public or private) on their own.
I agree that there is little difference in the end, but they are different scenarios.
A closer analogy would be the parents who stayed at home and kept their kids in the attic with them. The mayor has means at his disposal but we don't live in a nannystate and require the approval of the mayor to do anything for self-preservation.
In this case it isn't the Mayor's fault. It's in a different jurisdiction. There are rules in place for those who operate nursing homes for evacuation and they failed to follow protocol.