Would there not be issues surrounding your character's interacting in one world versus the other? Grabbing unique items and all the loot from Game 1, for example, and then porting across to Game 2 with everything intact. It is not an MMO so things like Gifting items is just breaking the game design. A Level 1 character should not have a +3 sword because D&D assumes that wealth levels are broadly linked to XP levels.
Levelling and XP would be another problem. Charging through Level 2 encounters because you have become Level 6 elsewhere is not going to fun for everyone else unless they are of a similar level.
