A community manager on Blizzard’s forums explains that the characters I’ve spent dozens of hours playing in Diablo III, with even more dozens of hours potentially ahead, won’t be accessible in the Playstation 4 version.
While we think cross-platform play would be awesome, there are currently no plans to allow connectivity between PlayStation Network and Battle.net (this is pretty standard for most games that have PC and console support). As a result, the characters on your Battle.net account and PlayStation account will also remain separate.
In other words, Valve’s Portal 2 can do what Blizzard can’t.
There’s a certain point where you invest enough in a game that you’re not going to start over just because the developers have adapted it to a gamepad and your couch is comfortable. Diablo III has gone well beyond that point. Still, a Playstation 4 version will be great for people who can’t play Diablo III because they don’t have PCs. If you see any of them, tell them for me.