I loved both equally. PS1 for the single player experience and the N64 for multiplayer games. It's hard for me to give the edge to any because I had great third party exclusives on the PS1 (at least between both systems) like MGS, FF 7 - 9, Parasite Eve, Soul Blade, Tekken 1 - 3, almost every fighter from Capcom, Soul Reaver, etc. Plus, it had great first (and second) party stuff like GT, Bloody Roar, Syphon Filter, Crash, Spyro, Parapa the Rapper, Jet moto, etc.
On the other hand, multiplats looked considerably better on the N64, and while I liked Sony's first party games back then, I found Nintendo's offerings to be superior with respect to scope and quality. I owned way more games on the PS1, but I'm inclined to think I played the N64 more due to Goldeneye, Smash Bros. 64, Diddy Kong Racing and Conker's Bad Furday - Smash being the chief game among them.
So, for the single player experience, the PS1 was the system for me, but for the multiplayer vybe ... definitely the N64. I'll vote Playstation since I'm a Sony whore it was the system that had MGS, the game that more or less shaped me as an individual since primary school.
Playstation = The Beast from the East
Sony + Nintendo = WIN! PS3 + PSV + PS4 + Wii U + 3DS
