I owned both... collectively I probably spent more time playing with *friends* on the N64 than I did on the PSOne... but there were more "good" unique titles on the PSOne. The better hardware? Nintendo 64 by far... loadtimes were either completely nonexistent or almost, precious Z-Buffering (no twisted textures) and Anti-Aliasing. That said, games were longer and deeper on the PSX due to the increased storage capacity of the CD-ROM.
RPGs, Fighting Games, Platformers = PSX
Shooters, Adventure Titles, Platformers, Racing = N64
I understand PSX had Gran Turismo 1 and 2, but N64 had F-Zero (which was amazing), Beetle Adventure Racing, Star Wars Pod Racer, X-Treme G 1 and 2 and so on.
N64 straight beat PSX with Resident Evil 2: Full FMVs, high res graphics, load times - Pretty conclusive hardware comparison there. Another good tech comparison is "Forsaken": N64 had smoother, more consistent graphics, 4-player mode w/ 30fps constant and so on.
I don't believe the N64 *ever* saw a Street Fighter game. It had a couple of clunky fighters (KI:Gold, MK Trilogy) but for the most part lacked in that department.
If I had the choice to go back in time and pick between the two... I'd get a PSX (because I did, heh). Reason: I can mod it and download *ALL* games and burn em on CD-Rs... can't beat 50 games for $12.
N64? Probably won't need to buy it again, as it still used carts and therefore you can download ROMs/Emulators for it - Only problem is, I haven't found a single emulator that can take on MYSTICAL NINJA STARRING GOEMON (One of my faves of all time) or Goldeneye... and I'm using a Quad Core PC w/ 4GB PC1033 with a Geforce 9800: Curiously, we can run Zelda at higher-than-original res with modder's high-res texture pack at 30fps or more, but for the most part? N64 emulation's got a ways to go... unless I'm horribly mistaken in which case please PM me the details
SEX.