Let's see here....
Xbox Live
Halo
Some multiplats that the GameCube didn't get (Star Wars: Battlefront, GTA, etc)
I really don't think anything more needs to be said on why the Xbox won.
The GameCube WAS beating the Xbox until late 2004. I bet we all know why the Xbox moved past the GameCube at that time.

Xbox live. It played DVD movies (still big deal at the time.). Way more games, and dominant in the shooter genre. Way better marketing. Better controller. Nintendo memory cards were criminally overprice, charging more for 1/8th the storage. And Halo was a big deal.

Halo, hard drive, xbox live, dvd. It truly showed something _new_ and was not a gimmick. It had true enhancements to what we knew of console gaming. Despite that, it was a failure btw.

It wasn't a failure, it was hugely successful for them in terms of what their goals were. They never expected to make money or be the leading console, they were up front about that at the time which was pissing investors off big time as they were saying it was a long term bet and it worked.

Lack of 3rd Party Supp.... oh wait :p

Must be Halo then

Halo helped but Nintendo also accidentally sabotaged the Gamecube's sales by overestimating the demand one winter and customer and retail confidence in the machine took a hit because they had to temporarily halt production on the console because their warehouses where full.

Also they were going through a period like they are going through now where the fanbase wanted to lynch the people in charge because of them murdering everything Zelda stood for by releasing the "kiddy" Wind Waker and its bright colorful graphics and super deformed characters. Who cares if they game was great the graphics ruined everything.

This opened my eyes to something... save the phenomenon of motion controls with the Wii that reached massive audiences, people have lost interest in Nintendo consoles way before the Wii U.

Holy shit! It's not Wii U's fault. Except for the hardcore fans, people have generally shifted away from Nintendo since the Gamecube days.

Also the reputation. Xbox was a console for adults. They had grown up with Nintendo and Sega, but now they could get their own adult system.

Game cube was for 'kids.' While Xbox and Playstation 2 had games for adults.

At least that's the perception.

It was just way ahead of it's time. You have XBL, a dedicated friends list... Halo 2 etc. Gamecube was considered "kiddy" at the time, and thus, sealed it's fate.

Your not wrong in ters of their goals, but it was a giant hot mess.  I was a fan of the thing and waited with bated breath at what its entrance would bring to the rest of the field.  Still it was a costly entrance.

The PS2 still trounced everyone else.  If it werent for the Wii phenom it would have been truly interesting to see the X360 and PS3 duke it out together on an even playing field (PS as a PlayStation fan I think the X360 was better for most of the gen).