Nothing specific sold me on the PS4, really, other than that I've been a fan of the PlayStation brand since the first console.
It's my favorite brand in today's video game consoles (due to the catalog of exclusive titles). All the cool new PS4 features are just a bonus.
I still buy / play other video game consoles and I even plan to eventually get an Xbox One, too.
Well, what stuck out to me most of all started when Microsoft started talking about 24 hour connection checks and cloud gaming technology. I don't have great internet at home, you see, and that kind of situation would've left me unable to play the console for more than 4 months out of the year (college student). So, PS4 got me initially on the fact that I could play it wherever I wanted. Now. while the 24 hour connections aren't required, you can still tell that the games at launch and in the first year were still designed around the premise of internet (Fable Legends), and frankly half of the features for the Xbox One I just can't use (like the TV thing. I don't have a box or cable).
The PS4 is just more of what I'm looking for. I can't use a good chunk of the Xbox Ones features, and games requiring internet won't work out too well for me.