The only time a MS console has surpassed a Nintendo one thus far is the original Xbox (well and Wii U if you count that) and this was largely because of how much Nintendo dropped the ball with those consoles, and even then it barely edged it out Cube by a couple million.
How did Nintendo drop the ball with Gamecube?Â The hardware seemed fine, more powerful than the PS2, the most comfortable modern controller I've ever had in my hands, solid 3rd party support, solid in-house support.
The Xbox achieved rough parity with Nintendo because they had an excellent exclusive lineup, the first good online service, the best hardware (original controller excluded), and Halo kicking them into high gear out of the gates.Â I'd give Microsoft its props for successfully breaking into the industry more than marginalize Nintendo for trying one last time to compete head-to-hear with Sony before abandoning the spec wars and going niche.
I like really the Gamecube in its own way (hell it's in part of my name), but it had plenty of flaws. Weird controller, lame lunchbox design, mini disc format, and not a particularly strong library overall, even from Nintendo. Even most of the quality games the Cube did had had sort of a niche appeal (Tales of Symphonia, F-Zero GX, Eternal Darkness, etc). Didn't have a great mainline Mario or Zelda game until the final months of its life with Twilight Princess.
I also saw the Gamecube as Nintendo trying to play Sony/MS's game rather than just do their own thing, (emphasising horsepower and similar style games) which they don't excel at as much as their NES/Wii route of being more distinct. Despite it being weird in design it was still largely a red ocean console, and this was just too crowded of a battlefield in the early 2000s.