I've heard in rumors that PSN and XBL users will be able to play cross-console/cross-company with each other. I do not know if this is confirmed or true but if someone does know, please let me know (preferably a Bungie employee).
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No. Sony has most of the market. It would be a disadvantage to them to allow xbox players to play with PS players, as a big selling point of Destiny is buying it on the system everyone else is playing on.