Without a doubt PS1.
Just like Ka-pi96 said, PS1 had the much better library of games, both in terms of quality and quantity!

N64: much better graphics, best controller ever made (you just had to change settings in shooters to Turok style controls), much better games, many of them are among the best games ever made cording to Metacritic. The only downside was the lack of JRPGs. Best multiplayer console ever made.

PS1: extreme ugly, nearly unplayable graphics (looking good on emulator only), but more games and tons of very good JRPGs.

Funny that you posted this recently, my PS1 died when I tried playing Legend of Dragoon for the first time last night. ;-;

Anyways N64 is a great console, but I have fond memories with all the Crash Bandicoot games, so PS1 for me.

PS1, because of all the RPG games, Crash, and Spyro. Although the N64 had Zelda, Mario 64, Maro Kart, Pokemon Stadium and Donkey Kong 64. I loved both consoles as a kid, to be honest.

When did I say blast Corps as the best game on the 64. In fact I hardly ever hear anyone talk about it anymore. 

In fact there are many games "better" than blast Corps on the 64. Mario 64, oot, goldeneye, wave race and many more. I was just saying that it was a game I really enjoyed. 

But as you said games are subjective. What 1 person enjoys another thinks is rubbish. One thinks Sony is the best console maker.  Others Nintendo. Others Microsoft. 

Therefore when I say "you" I meant me. I think if you went and got gamerankings for the top 10 games on each console(n64 and ps1)   I think the 64 would win. But again it's how people feel and people will generally sit on 1 side or the other. 

PS1 has aged better. Theres alot of good PS1 RPGs.

at the time I loved my N64 simply for mario64,.... but even that game isnt able to put it above the PS1.
PS1 had so many good games compaired to the N64, and wins by volume of games.

Playstation one was the console that got me into gaming, most of my favourite games were released on it.

Hard call to say which is best from the top10.... also a game console is more than just its best 10 games.

PS1 wins by amount of Good RPGs though:

Alundra 1
Alundra 2
Arc the lad 1
Arc the lad 2
Arc the lad 3
Beyound the Beyond
Breath of Fire 3
Breath of Fire 4
Brigandine Legend of Forsena
Chrono Trigger
Chrono Cross
Digimon World 1
Digimon World 2
Digimon World 3
Dragon Quest 7
Eternal Eyes
Final Fantasy 4
Final Fantasy 5
Final Fantasy 6
Final Fantasy 7
Final Fantasy 8
Final Fantasy 9
Final Fantasy Tactics
Front Mission 2
Front Mission 3
Grandia 1
Guardians Crusade
Jade Cocoon
Legend of Dragoon
Legend of Legaia
Legend of Mana
Lunar 1  Silver Star Story
Lunar 2 Eternal Blue
Langrisser IV
Persona 1
Persona 2,  Innocent Sin + Eternal Punishment.
SaGa Frontier 1
SaGa Frontier 2
Star Ocean The Second Story.
Suikoden 1
Suikoden 2
Saiyuki journey west
Tales of Destiny 1
Tales of Destiny 2
Tales of Phantasia
Thousand Arms
TearRing Saga
Valkyrie Profile
Vandal Hearts 1
Vandal Hearts 2
Wild Arms 1
Wild Arms 2
Xenogears

and Im probably missing a few RPGs here and there.

N64 - easy win. Ocarina of time (BEST GAME 99% on metacritic), Pokemon Snap, Pokemon Stadium, Mario 64, Goldenye 007, DK64, Perfect Dark, Diddy kong racing, Banjo Kazooie etc

PS1 had some good looking games too.