Strictly speaking, New Orleans isn't coastal. We're 100 river miles upstream from the Gulf!
Charleston actually has a higher annual risk of flooding than New Orleans. New Orleans hasn't had a major flood since Katrina while Charleston, Houston, New York, Miami and even major inland cities like Nashville and Denver have had multiple. NOLA has to be one of the most climate-resilient cities in the U.S., given we have spent billions of dollars on levees, flood walls, and pumps. Charleston has no comparable infrastructure.
However, the idea that New Orleans exists on borrowed time (i.e., "is sinking") is a big part of the city's foundational mythology. The original French settlement was expected to fail because of bad land, malaria, Indian raids, etc, and that sense of a place that
isn't really suppose to be here is what gives New Orleans its irreverent, gothic sensibilities. Charleston could never.