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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Not possible, microsoft and Sony would never do that. It would be cool and could possibly let you play with friends on a XB1 when you rather play on a PS4, but it'll never happen.