I also had both, so I'm pretty much even. Both had its pros and cons, though I would lean slightly more to the Nintendo 64 side.
Playstation packed a lot on to those discs and many claim it to be the more graphically powerful of the two. It basically defined RPG's, being home to several Final Fantasy games, among many many others that I won't bother to mention. On the flip side, I absolutely hated the load times.
That's an area where the N64 shined. Hardly any load times as a result of using carts. It also blew Mario up. This was the first time we saw Mario in 3D action, with Super Mario 64 being the most famous of his titles. The Nintendo 64 was also home of one of the best games of all time (some say THE best game of all time), Ocarina of Time. Plus it had some pretty kickass multiplayer games, like Super Smash Bros, Mario Kart, Mario Party, Goldeneye, Perfect Dark and Star Fox. It put many of Nintendo's franchises into the spotlight and provided a significant stepping stone for them to develop into the great games we see today (Brawl anyone?).
Yeah, I'm probably a bit biased towards Nintendo, but hey, I did have both of those consoles and simply enjoyed my N64 more.