I love the ps4! My favorite thing about it is probably being able to turn it off and go where ever and then turn it right back on and continue playing where i left off.
As for the xbox 1, I'm sure they are equally as good if you are an xbox fan, however, i never used my 360 much so it was easy for me to choose. I do know the specs, for the most part, are better (or higher) on ps4, however, those specs are small things that no one will be able to actually tell between the two devices.
The ps4 does record 15 mins vs the xbox's 5 mins if you like to upload videos. I dont use it, but it's kinda neat to play with.
A few of the games right now you can pay $10 extra and upgrade your ps3 game to ps4. And sometime in the next couple of months they are supposed to be pushing a cloud gaming where you can upload your ps3 games that you've purchased and still be able to play them on ps4. they're not backwards compatible, but you can save the game to your hd and play it that way.
One disadvantage has to be the controller, the battery life is nowhere near the battery life of the ps3 controller. That's just getting nitpicky really though.