In Pokemon Diamond, Hypnosis has 70% accuracy. In Pokemon Platinum, it has 60%. In a battle between these two games, which value is used?
It depends on the host game. If Platinum is hosting, it will be 60%; if Diamond is hosting, it will be 70%.
On a Wi-Fi battle, if a Plat cart hosts the game, then Hypnosis' accuracy will be 60% for both players, EVEN if the other guy is using D/P. If D/P player is hosting, Hypnosis will be 70%, even if the other guy is using Plat. (source)