Saturn.
It's somewhat close, but I'll make an argument for it over the PS1 for the following reasons:
1) Most of the best (non RPG) PS1 games, whilst groundbreaking and revolutionary for their time, haven't aged the best. This is due to a combination of being superseded by superior sequels/clones, utilising outdated and clunky control schemes and mechanics and ugly 3D visuals. That's not to say they're unplayable by any means of course. I can still get plenty of mileage out of them. But the Saturn is primarily known for great 2D games, and they're virtually all just as fantastic now as when they were released, both visually and playability wise.
2) It has an unbeatable library of 2D shooters and 2D fighters which are two of the best genres for sheer intensity and depth of gameplay, meaning they have a lot of staying power.
3) It has the best controller ever designed for aforementioned 2D goodness.
4) AM2>>>Namco, and this was a pretty big deal if you love your arcade games (which you likely do if you enjoy games from this era).
5) Although the PS1 was undoubtedly king of the RPGs for the 5th gen, the Saturn had a very solid library too, especially if you include imports (an increasing number of which are playable in English). I would actually say that the best ones on the Saturn (Panzer Dragoon Saga, Shining Force III parts 1-3, Dragonforce) have an edge over the best ones on the PS1 (Chrono Cross, FFIX, Suikoden II, Persona 2). Given that I have a job and other hobbies/commitments, I obviously don't have time to play EVERY great 30+ hour game on each system. A better approach is to pick a handful of the best for each console, and the Saturn wins in this regard for me.
N64 is a very, very distant third. Easily Nintendo's worst major console. Meagre library, very little genre diversity, one of the worst controllers ever designed (this, combined with the hideous framerate of most games, means they mostly play like absolute dogshit now). Yes Ocarina of Time, Majora's Mask and Mario 64 are amongst the GOAT. But then, Chrono Cross, Panzer Dragoon Saga, Radiant Silvergun, MGS etc. are probably amongst the best games of their respective genres too. And the Saturn and PS1 each had tons more great games than the N64 outside of that. Some of the other celebrated N64 games have just flat out aged badly (Goldeneye/Perfect Dark), whereas others were simply never that great to begin with (Starfox 64). After the Snes, which is probably the GOAT console, I'd have been pretty fucked off about the offerings I got on the N64 if I was a Nintendo fan back in the 1990s (once the initial OMG IT'S MARIO IN 3D hysteria had worn off) and would probably have jumped ship to Sony.
Finally the people saying things like "anyone saying X obviously hasn't played Y/is just trying to be a hipster" aren't contributing anything worthwhile to the discussion which, lest we forget, is about which system YOU would want to play, not which one is "objectively" the best (whatever that means). I mean I can't for the life of me understand why anyone would say the N64 was the best console of that generation, but I'd at least give their opinion credit for being an authentic and genuine one. I also notice that the ones who are the most obnoxiously smug in the superiority of their own opinion tend to also be the least knowledgeable. A good example is this guy:
I legitimately think anyone answering anything other than PS1 is an edgelord here (Or didn't own one and is fighting the good console warrior fight 20 years later). MOST of the games for all three of these systems haven't 'aged well' by most standards, but the PS1 was an embarassment of riches for gaming. Multiplat was barely even a thing that gen, so it is probably something like an 85-10-5 split in terms of percentages of good games back then, PS1-N64-Saturn.
who says that anyone voting for a non PS1 option is an "edgelord" but then goes on to make the claim that the N64 has twice as many good games as the Saturn, which is embarrassing and laughable quite frankly. Oh, and multiplat was very much "a thing" back then btw...
A little humility goes a long way. Pontificating aggressively on subjects you're obviously clueless about makes you look more than slightly foolish. Just a friendly tip