The show is very loosely related, as rather than a nuclear war the ship takes part in, there's a pandemic that devastates the world that the ship is coincidentally protected from by isolation.
It was pretty ok but not good imo. Too much emotional introspection by the narrating character, the captain. Not enough action or detail in the society building.
Never heard of the TV show. I'm sort of afraid of watching it, kinda like the Timeline movie based on the Crichton novel.