Agree with Atlin. We have both as well, and regardless of your situation, PS Plus is worth it.
Obviously the PS3 is cheaper, as it's older hardware and used ones are easy to find. Game library is big, and most of those games are cheap now. Though the number of new games coming out is dwindling. If cost is a concern, this is probably your better option. You won't run out of games to play for a while. Also it has Okami HD as a download on PSN.
PS4 is more expensive, but more powerful, more features, and new games are coming out for it. More expensive overall, but as Atlin said, wait a bit and prices will drop as used copies of games become available. Smaller (but growing) library, with good games like Alien Isolation and Shadow of Mordor.
It comes down to your priorities and concerns. If you do get one, find me on PSN.

Oh, last note: whichever you get, buy the pertinent version of The Last of Us and play it, play it, play it. I think both systems have a bundle which includes it.