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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Deej has said... definitely not. Even different generations of the same brand cannot play with each other. This means PS3 and PS4 cannot play with each other and neither can Xbox 360 and Xbox One. What you CAN do is a one time offer of upgrading your Guardians from PS3 to PS4 or Xbox 360 to Xbox One. Other than that... you are walled away.