the advantage of the xbox controller is games will correctly display hint buttons, like on QTE shit. A few games can do it for the PS4 ds controller but most don't try. i would be careful of trying to use bluetooth with DS4, i dunno if its still true but before you had to install this shitty driver that would bluescreen me a lot and it had some shitty adware built in too i think. Wired DS4 works fine of course. Maybe Windows 10 will have better wireless support.
i had a wireless 360 for a long time, worked great. switched recently to wired xbox one, i like the big ass controller but it does cramp my hand more than DS4.