The last console generation was a pretty lopsided time of misnomers and missed targets:
The Gamecube had 'party games' written all over it, but the only party games made were Mario Party, and what few other multiplayer games it had were way too high-concept to be marketable (Zelda Four Swords and Final Fantasy Crystal Chronicles). It ended up being a kids console... a whiny, bratty kids console.
The Playstation2 was the all-rounder, attracting the largest number of casual gamers. Madden and GTA outsold Final Fantasy games, but RPG fans never felt smothered by it. Sony kept the largest and most eclectic library of games, so it was almost fanboy-proof.
Then there's the XBox. One would think that between the kid-friendly 'Cube and the ho-hum average 'Station2, the XBox would become that 'elitist' console, kind of like what the Dreamcast and TurboGrafx were. And while that is technically what happened, the 'elitists' that became the XBox's would-be discerning demographic, turned out to be 18-35 druken male frat-boys who couldn't get enough Halo to save their little passive-aggressive homophobic lives. Before long, any game that wasn't a First Person Shooter with online multiplayer was relegated to the bargain bin. The XBox library is full of one-hit wonders like Brute Force, Xyanide, Gun Valkyrie, Armed and Dangerous, and Panzer Dragoon Orta. Otogi just barely managed to get a sequel, and don't even get me started on Oddworld: Stranger's Wrath.
The XBox had all the marks of greatness: It was a powerful console, it was relatively easy to develop for, it had a solid online component, and it attracted virtually equal numbers of eastern and western developers. Sadly, it just got bogged down by a mediocre majority who wouldn't take chances on unique games.
I find it slightly vindicating that the XBox 360 by contrast has achieved a far wider demographic than its predecessor. Sure, the drunken homophobe frat-bastards are still there, but they're drowned out by everyone else... so long as you stay off voice chat.