How do you top the beautiful, poetic experience that was ThatGameCompany's Flower? Easy, just make a game that strips away everything annoying of maddening modern online gameplay and set it inside a lush gameworld that looks like a living painting. The travels that you undertake in Journey culminate in an incredibly touching moment. It's not just one of the best PS3 games. It's one of the best games ever, period.
Mass Effect 3
Chose multiple classes and races, play co-op, save planets from insane alien races and have many options on how you want to play the game. Mass effect 3 is the final installment in the trilogy from BioWare and is sure to keep old and new players alike wishing for a fourth. As one of the best PS3 games of 2013 this would be the title to pick if I could only play one.
For the PS4, you can play PS3 games via streaming service PlayStation Now, but it doesn't come cheap and fails to take into account physical and digital games you may already own.
Sadly, you can't just play your old PS3 games on PS4, neither by inserting the disc or downloading them again from PSN. The systems are fundamentally not compatible with each other.