In terms of best library overall, I have to say the PS2 wins, but not by a wide margin.
The PS2 absolutely dominated the scene in its day. The original Xbox, Gamecube, and Dreamcast while they had some amazing S-Tier titles back in their day, weren't all that great overall.
PS1 also has a great library, especially if you're an RPG fan. On the flip side, Nintendo's N64 dropped the ball, and the Sega Saturn was pretty lackluster with no staying power.
Going back just one more generation and now you have an amazing bunch of platforms. SNES, Genesis, Neo Geo, and TG-16 all head to head in that order.
Going back one more, and NES just straight up dominates. Does anyone even remember the Master System?
My personal list goes like this.
PS2
SNES
PS1
NES
Gamecube
Genesis
Xbox
Dreamcast
Neo Geo
TG-16
N64
Saturn
I guess after Saturn it's basically a tossup between Master System, Atari 2600, ColecoVision, Intellivision, 3DO, and CD-i?
PS3/PS4, 360/One, Wii/WiiU are too "new" for me to call them classic yet.
Edit: may as well add my opinions on handhelds too.
Nintendo DS
Game Boy Color
PSP
Game Boy Advance
Game Boy
Game Gear
3DS and Switch are too new for me (yeah, Switch is a handheld not a console...fight me) and so is Vita.....I guess N-Gage belongs up there somewhere too.