>>717603882 (OP)My vote goes to Xbox.
Sony sold the most units because it was also a DVD player but the Xbox had the bigger effect on gaming as a whole in that gen. That is why Sony made a conscious effort to imitate it more in the PS3 next gen. Xbox had THE killer app of the era (Halo) and the PS2, while it had a very large game library, never had anything that could match the sheer hype and influence on the gaming landscape that Halo had for shooters (which to this day are THE dominant genre next to RPG games, which were also wider in scale on the xbox than anything before it.)
Gamecube was also very influential with many very good games on it, but worse sales. Dreamcast went hardest into this and had a lot of cool features and games, but ultimately made very little impact on the gaming sphere as a whole and sold poorly.
If measuring by sales, PS2. If measuring by impact on Gaming tech and genre popularity, Xbox. If measuring by long term cultural impact, Gamecube. There is no scenario in which the dreamcast wins. It did what the other 3 did, but not as good as any individually.