Im not sure i understand the question. Every home theater system should be compatible for either.
As far as the bluetooth question, you will just have to shop around, most new ones have it.
As long as a home theater in a box comes with a receiver that has an optical in on the back, you are set up for either xbox or ps4. if it has hdmi in that might be better since you wouldnt have to change the input on the tv every time you switch video feeds.