have you taken a look at the videos reviewing these consoles and the games they play? They all look fantastic, we've left the "old" graphics realm for more than a decade now, anything that runs on the PS3 will already look amazing.
that being said, if you have a budget of 600 bucks go for a PS4, once they're in stock again a bundle will cost maybe 400-450 bucks at your local target/walmart/best buy/random store. Then you'll still have 150-200 left to get a bunch of games (or save up for upcoming games, some of which look amazing like Watch Dogs, Destiny, Dragon Age: Inquisition, Final Fantasy 15, etc)
If you build a PC you can get a nice mid ranged PC for 600 bucks, but that requires some things that you may or may not already have...