Oh, the N64 was a brilliant system! Down right amazing. It had way more power than its contemporaries. Anybody who owned one knew the brilliance of the system, but those who did not missed out on a lot. Back in the day we had so many debates over why one console was better than the other. The PSX had it beat in two major places, the PSX was easier and cheaper to develop for, and thus had a vastly larger library than the 64. As far as number of titles, the PSX won that hands down, the 64 couldn't even pretend to be competition from that standpoint, which was unfortunate for it. The other area that the PSX had it beat hands down was capacity, the PSX disc had a whopping 600mb from the beginning (though it rarely used anywhere near that much space except when it was chock full audio and video), while the N64 cartridges only had 64mb. Which makes it even more amazing that so many 64 games looked so impressive while PSX games always managed to look like pixelated crap. PSX games also had the ability to contain full motion video and CD quality audio, which the N64 could barely dream of ever doing (to see how that dream eventually turned out, take a look at the port of Resident Evil 2, two whole compact discs compressed onto one cartridge and it managed to look even better than it did on the PSX, too bad they only managed to do this when the console was on its death bed).
When you take a look at amazing games like Ocarina of Time, Goldeneye, Perfect Dark and many others, and consider them in light of the consoles limitations (mostly due to the small cartridges), any arguments for the PSX being the superior machine fly out the window. While the N64 had a shamfully small library on account of the difficulty the cartridge system cause developers, the good games it did have were really good and lightyears ahead of anything on the PSX.
As mentioned before, most really good PSX games also had a far superior PC version.
The controller was also wonderfully unique, while the PSX controller was basically the same sort of thing all previous consoles had, the N64 controller really went all out to do something new, and obviously they did something right because the PSX redid their controllers with analogue sticks, and most controllers since then have gone with an analogue stick similar to the 64's. The "rumble pack", like the analogue stick, was another idea that began a new trend in console gaming. Everybody uses a vibrating controller now, having stolen the idea from the rumble pack.