Too be fair, the PS2 faced a lot less competition in its first few years. There was the Dreamcast and the remnants of the N64 market, but that's about it. The PS2 was basically in a competitionless vacuum so it could have explosive growth with nothing to stand in its way, and when the xbox/gc came out several years later the PS2 had already gained too much ground to be beaten.
The Wii was actually the last console on the market for this generation, so it had competition right from the beginning. I think that might make its success all the more impressive, because the PS2's success was like taking candy from a baby that hadn't even been born.