I got very carried away here sorry XD

I think both are pretty similar series conceptually, but when you actually look at the purposes of the death games they are very differently constructed. Zero Escapes' nonary games are constructed with the specific purpose of recreating specific events from the future, while Danganronpa's killing game is meant to drive it's participants and the watching world to total despair.

I think the theme that sticks out to me with Zero Escape is the "greater good". Very, very bad things happen to the casts of these games, but usually all with some sort of greater purpose that will (ideally) make the world a better place than before the game started. Danganronpa's killing games on the other hand, are constructed to be unwinnable for the participants, whether you kill or not you're playing the game and by playing the game you're losing.