At this point, it's nostalgia vs even older nostalgia for me when it comes to consoles. I still think there's a strong case for the NES and SNES. The former paved the way for video games to be more than a fad and a huge industry after the Crash of 1983, and pioneered some impressive technological achievements given the processing power on hand. The same goes for the SNES. Those cartridge-based games were really able to push the limits of their systems thanks to some of the cartridges themselves containing chips that allowed for primitive 3D graphics and the like. There are some true classics from the 8-bit and 16-bit era.
However, the PS2 definitely has a strong case of its own, given its sales, longevity, and library. Also, by that point, a mediocre video game still tended to be better than the mediocre games of earlier eras. That's not to say there aren't bad games on the PS2, but when you look at the really bad stuff on NES and SNES - the kind of fare that AVGN's classic episodes were built upon - they hold up a lot worse than disappointing PS2 games. Game design was in its infancy, so bad to mediocre games in the 8-bit and 16-bit era had
really clunky controls and gameplay mechanics, poor level design and unfair challenge to compensate for a lack of true longevity, and in the worst case scenario, were barely functional. By the PS2 era, the mediocre games were at least a bit better made, and more disappointing or uninspired than a complete disaster. In that respect, the PS2's library arguably holds up better overall, and that's a big factor in the discussion.
I obviously have a lot of nostalgia for the NBA Live series on PS2 from NBA Live 2002 through to NBA Live 06 (cheap plug of our ongoing
25th Anniversary of NBA Live content here), as well as the first three NBA Street games. The PS2-era GTA games are still my favourites in the series, with GTA III and Liberty City Stories being my top two (though Vice City, Vice City Stories, and San Andreas are all brilliant as well). A lot of the WWF/WWE games from the PS2 era are more fun than recent releases on superior systems, though they were admittedly still good in the PS3/360 era as well. Also, I know they're kind of looked down on now, but the Mortal Kombat games from the PS2 era - Deadly Alliance, Deception, and Armageddon - were all fun in their day. I still like them when I dust them off.
Of course, something that I miss about that era is the amount of content that just came with the game, and the complete absence of season passes and microtransactions. It's hard to grumble about that without sounding like an "old head", but those practices have stifled creativity and affected quality, as more focus goes on the recurrent revenue mechanics than making a great experience. With that being said, some of the WWE games had ridiculously long grinds to unlock everything, to the point where you were tired of the game by the time you unlocked it all. One of the games also required you to unlock Jake "The Snake" Roberts in the PSP version to unlock him in the PS2 version as well. Screw that; I invested in an Action Replay (the PAL Gameshark) and did it that way!
So yeah, I definitely have a lot of fond memories of the PS2. I think you bring up a good point about being able to buy more games as well. By the time PS2 came around, I had more of my own money to buy games, so there was much less renting. I'm trying to think of the last game I rented, actually. It might've been Conker's Bad Fur Day for the Nintendo 64, and I ended up getting that as a birthday or Christmas present not long after that anyway. I might've rented a couple of PS2 games at some point, possibly to try before I bought, but none are springing immediately to mind.