XBox was actually whupping the GameCube pretty badly before MS called it off.
Looking back at some NPD numbers, Nintendo had a great holiday 2003, when they dropped the GameCube to $99.99, but generally speaking the XBox was gaining momentum as that generation wore on, where GameCube was faltering, a sample of some months:
Aug 2004:
XBox: 216k
PS2: 211k (shortages)
GameCube: 108k
Nov 2004:
XBox - 708k
GameCube - 350k
Jan 2005 (RE4 launch):
XBox: 241k
Gamecube: 114k
May 2005:
XBox - 129k
GameCube - 50k
June 2005:
PS2- 355k
XBox - 168k
GCN - 70k
The XBox was routinely outselling the GameCube by 2-2.5x towards the end of the gen before MS pulled the plug. Had the XBox been given a proper 5-6 years on market, the gap almost certainly would've been bigger. GameCube would do OK in Nov/Dec, was a lame duck console most other times.