Diablo III will be transferable to the PS4 version

The other two new social systems are Player Mail (players can mail items to other players), and Player Gifts. Here, when a Legendary item drops, a second item will also drop with a friend's name on it.

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This item, of appropriate rarity and tailored made for any character the friend wants, will be delivered to the friend.
"So once again, we're not questing together,

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but we're still part of a greater world," Berger said.
It was also confirmed at BlizzCon this weekend (via IGN) that characters created on the PlayStation 3 version of Diablo III will be transferable to the PS4 version.
Lastly, Berger addressed the possibility of Diablo III coming to the Xbox One. He said, "For the moment,

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 we're only talking about the PS4 for the Ultimate Evil Edition."