Playstation and Playstation 2 aren't as great as most people make them out to be, I vastly preferred the N64 and the Gamecube, and the Xbox is a joke compared to the Gamecube.
My issues with the Playstation derive from the lack of analog control and horrible camera controls. Tomb Raider, for being lauded so much at the time, controls like utter crap now; Spyro and Crash are a joke compared to the tight, acrobatic controls of Super Mario 64; Star Fox 64 perfected the on-rail shooter genre (and is still the best as far as I'm concerned); Wave Race 64 made Jet Moto look hilariously bad in terms of control; Ocarina of Time had brilliant camera controls as well as fluid controls; yada yada yada. The Playstation was a novelty that finally opened games up to cinematic cutscenes, but IMO that's just about all it did. I refuse to replay the majority of Playstation games today, unless they fall under the category of JRPG or 2-d sidescroller. The N64 may have had fewer games, but it has far more timeless classics.
With the PS2, I felt that the majority of games were merely good, not great, much like how I feel about the Wii. More importantly, however, I felt that the best of the Gamecube was on an entirely different level compared to the best of the PS2 and Xbox. F-Zero GX and Mario Kart: Double Dash are phenomenal arcade racers with insane amounts of depth, Sunshine an excellent (albeit short) platformer, Melee the only fighting game I've ever become obsessed with, and Metroid Prime an unbelievably new experience. While there are PS2 games that are among my favorite games of all time (MGS2, ICO, SOCOM 2), there just aren't enough for it to be my favorite console of the generation. It doesn't help that I like Skies of Arcadia and Paper Mario 2 far more than all of the RPG's I played on the PS2.
It's all my opinion of course, I'm sure my tastes are far different than others.
While many PSX and PS2 games will have a hard time playing as well as you remember them or whatnot, the sheer amount of games on the Sony systems made some definite games appear on the systems. The N64 and GC had some amazing titles, but suffered from the majority coming from Nintendo themselves. As you already pointed out in your post. WHereas I can point out the same amount of good games on the PSX or PS2 from third parties. Not saying any 'X' games on the PS2 is better than any 'X' game on the GC, just the facts that the PSX and PS2 saw 10x the amount of games and as such, still got plenty of good games (and bad ones).