Are you a BMW or Audi fan, a Jag man over a Lexus, it's all about personal preference. Games set apart the two consoles and have done for years. Yes the PS4 is more advanced and geared around gaming, rather than TV.
I've never got on with the Xbox series, had two and just couldn't live with them, and it's purely down to the experience. I've owned every PS made, I'm a launch man and love my console.
Me personally as a heavy gamer, the PS4 wins just for the fact the quality, comfort and overall experience of using a PS4 makes me happy. As Will has said if you have friends on a different console it makes sense to move. Gaming is no longer a single player experience, with online gaming you all need the same console. Although I heard that during Ghosts the clan wars were a mix of PS and XBOX gamers, whilst not interacting within the same game, the war results were a combined.
Graphically yes the PS has the upper hand, but as above its not just about graphics. Saying that the differences are marginal. Yes there's more graphical detail, but as Dan says you won't see the difference once you're playing.