How different are "Kill Doctor Lucky" and "Save Doctor Lucky"?
Save Dr Lucky is similar in some ways, but does play differently. In order to increase the chance of success as the game progresses, the board shrinks one deck at time as the Titanic sinks, which means forces the players closer together. This can be annoying when you are holding on to room cards for a lower deck that has just sunk.

It is definitely worth owning if you enjoy Kill Dr Lucky. I will say that it doesn't play very well if you don't have at least four players.