Blizzard Entertainment has confirmed that the PlayStation 3 and PlayStation 4 versions of Diablo 3 won't link up with Battle.net, which means no cross-platform play using your profile on the PC side. Word comes from Blizzard community manager 'Vaeflare' speaking on the Battle.net forums, as spotted by Shacknews.
The post also confirms that there's no plan either to add gamepad support to the PC version of the game. Similarly, the console versions will not support USB-connected mouse/keyboard controls. ShackNews rightly notes that this console take on Diablo 3 is clearly a different game, with new elements such as a dodge move. It's unfortunate that the console and PC versions of the game aren't part of the same, unified network, but it's not all together surprising.