PS1 and N64 are a close tie but I didn't own an N64 and could only play it at a friends.
PS1 offered great games from Metal Gear Solid and Resident Evil to Ape Escape (personal favorite) to Spyro and Crash. Such a fantastic system. Of course there's also Final Fantasy 7 and Parasite Eve. Soul Reaver and way too many to list.
Though the N64 had Mario Kart, Golden Eye, Jet Force Gemini, Pod Racer, Ocarina of Time, Mario 64, Banjo Kazooie, Perfect Dark and more. Plus it had better in game graphics and multiplayer over all. I guess it's kind of the better system in many aspects but I had the PS1 and loved it! There's a lot of underappreciated gems on that system like that open world Batman game and even that awesome Small Soldiers game which had some fantastic multiplayer up there with Twisted Metal.
