Would either one be in your office/room? Or would the TV go to the living room?
Just depends on your needs. For console gaming, I would lean towards the TV. Nothing wrong with the monitor if you're a pretty private person, but if you ever hope to have a living room session with friends you'll benefit from a TV. It's also nice to curl up on the couch with a controller in your hands.
And even if you don't have cable TV or anything, Netflix and Hulu apps will always be enjoyable in the living room.