I usually say the PSX was the best console of all-time. Though when I have this discussion with my gaming friends, they tend to gravitate toward the PS2.
Anyway, I would normally point toward the sheer variety and number of titles as evidence for the console's greatness. In a conversation with most of my gaming friends I feel as though if I were to ask 50 people for their favourite PSX title, I will likely hear back 40 different answers, and often they will recite the names of games I had previously never heard of.
A quick look on gamerankings.com (not analyzing duplicate or multi-console releases) reveals about double the number of games with an aggregate review score of 80%+.
Just the last few months I have played through FF7 again. I just finished Resident Evil 2 again, and am half way through RE3 (that fucking Nemesis gets the heart pumping) and am being thoroughly entertained by Crash Team Racing (which I never played at the time of released, but enjoy more than MK64 but probably about equal to how I remember Diddy Kong Racing). After RE3 I will play through Dino Crisis and Vagrant Story (I never did finish Vagrant Story all those years ago).
No doubt N64 has amazing games, and the argument could of course be made that the great N64 games are better than the great PSX games (I disagree, but whatever), but the sheer volume and variety of great games on PSX are undeniable.