What is the accuracy of Hypnosis in a battle between Diamond and Platinum versions?

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)