PS4:
-Hard Drive can be upgraded by sliding off the top cover, opening up a few screws, and putting in the new hard drive
-More focused on gaming
-Controller feels a bit more better (personally. I've held both controllers, and I find the PS4 more fitting. For my hands atleast)
-Smaller and doesn't take up as much space
-Starts up faster
-Cannot use external hdd to install games on
-Has PS2 game emulation (Doesn't read PS2 game discs, you have to buy the games off the PS store for a cheap price)
-Doesn't read CDs
-Might become 4k with the rumored PS4K console
-Getting virtual reality
-Has 2 USB Ports (A usb hub can be purchased to get even more ports)
-Has rest mode (System is semi-turned off, lower power consumption, can charge controllers and other devices, can download firmware updates and game updates, no fan activity in rest mode, maybe a bit but VERY hard to tell)
-Power supply is internal, no power brick required
-Uses newer ram
-Usually has most framerate and slightly better graphics than the xbox one (only on some games)
Xbox One
-Can use External Hard Drives to install games on
-Hard Drive cannot be upgraded, you would have to buy a new xbox to get a bigger storage amount
-Supports backwards compatibility for some 360 games
-Can be slightly quieter than the PS4 sometimes, has more ventilation
-Only has 1 usb port on the left side of the console, and 2 on the back, makes it 3 but would be better at the front (hub can be purchased for more ports)
-Can be used to watch tv
-More entertainment focused, a bit of gaming
-Requires AA batteries to use controller (Charge and play kit needs to be purchased to charge batteries and play)
-Uses older DDR3 RAM while PS4 uses newer ram
-Has power brick on cord
-Kinect, can be used to turn system off with voice, turn off system, etc.
Now compare all the info together and see which one you find better