The OG Xbox did sell more units than the Gamecube (~24 million vs. 21.7 million per Wikipedia anyway), but these seem close enough that it's a bit weird to classify them differently. I guess one way to justify that outlook is that Microsoft was coming from nothing in the console space, so getting to a distant 2nd place (even if only narrowly) makes for a decent start whereas the Gamecube sold fewer units than the N64 even while the home console market was growing as a whole.
Part of why they are considered differently is that the Japanese market ignored the Xbox and has continued to more or less. If you look at just the U.S market, the Xbox was very competitive in the first generation. Halo in particular was huge in the U.S., and completely changed gaming and the first-person market forever.
Nintendo Gamecube: 22 million (PS2: 155 million, Xbox: 24 million)
Nintendo Wii: 101.63 million
Nintendo had very high targets for Gamecube, hoping to make up for some of the "lost ground" of the n64's weaker sales compared to its predecessor. The Xbox struggled heavily in Japan compared to Nintendo, and was a newcomer to the console scene, but still made more total sales.
The Gamecube also had an extra year before Nintendo released a successor compared with the Xbox. Both came out around the same time, but the Xbox 360 was released a full year before the Nintendo Wii. Luckily for Nintendo, the Wii ended up being very popular compared to the Gamecube and sold ~5x more consoles.
I think both original Xbox and Gamecube had sales targets higher than what they ended up reaching, but you could make an argument that Nintendo failed to capitalize on their previous popularity and market share and had a bigger flop.
I agree the sales were close, but I think the narrative/momentum was very different for the two. That was Microsoft's first console. They started with nothing, and by the end of the generation had sold more than Nintendo and established critical IPs and an online service for the next generation. Nintendo, at the time, felt very backed into a corner - which of course gave us the Wii that shattered all expectations.
I would classify them differently. I mean they were both not very successful consoles, but the Xbox was at least a first effort from a new competitor. It makes sense that it was… more of a predictable learning experience.
The GameCube seemed like a surprisingly poor showing from such an experienced company. But hey, hard to give them too much flack given the follow up. Guess the GameCube was a strong unexpected learning experience.
