This is no real contest.
The N64 is obviously the more powerful console. Not only on paper in most aspects, but also in the real world. The only real thing the PS1 had on the N64 that truly hindered the latter on the technical side was of course the capacity of discs versus that of cartridges. Which meant some things would be cut or quality compromised. However, a technically good game for N64 easily looked a good step above one for the PS1. Always, it's undebatable. Sadly there were however too few developers that actually wanted to use the N64's power, which is why you have utter graphical crap like Superman 64 on a console that also had Conker's Bad Fur Day.
I'm not hating the console though, in fact, the PS1 is still my #2 favorite console of all time.
As a side-note, I'm glad Nintendo choose cartridges instead of discs. CD's still weren't really 'there yet' back then and even if it's my second favorite console, it was also the one that gave me the most problems with my games. Durability of the discs was bad and those load-times...
