When Atlus first revealed Dragon Crown's release date, the publisher said that cross-platform play simply wouldn't be possible. Thankfully developer VanillaWare seems to have overcome the technical hurdles to and is bringing Cross-Play between PS3 and Vita in a new patch, due soon.
Atlus confirmed the cross-play patch yesterday. The patch will allow PS3 and Vita owners to join each other's sessions. However, although the game supports cross-play, there is no cross-buy. You'll still have to buy each game separately on the PlayStation Store.