A:AnswerHey detriana99,
I just took another look through the spec sheet; it doesn't appear to list battery life anywhere. There are no battery-life-dependent items in my experience with the headset, as the headset requires a USB port to plug into for power.
A:AnswerIt is compatible with the PS4 but not all the functionality of OMEN Command Software (you can adjust the headphones via a windows based computer though and then plug into to PS4. The sound is awesome and voice chat works. Keep in mind it is USB so you might need a USB extension. The ear cups stay cold too. I don't know about the XBOX.