I think it's less a matter of sales and more a matter of the games. XBox as the generation went on got ports of some of the big PS2 games like GTA and Metal Gear Solid 2, games that never came to Gamecube. Then there were the multiplats that came to Xbox and PS2 but skipped the Gamecube like the Star Wars Battlefront games. And lastly, there were the ports of high-end PC games that only came to Xbox and nowhere else like Morrowind, Far Cry, Doom 3, and Half Life 2. In the first year there would be games that came out on PS2 and Gamecube and skipped the Xbox like the 2002 Clone Wars, which was ported later, but by the end of the generation things had really flipped and Xbox did what no other 2nd-place console had been able to do in locking up that much built-in third-party support. Even with 150 million units sold, it didn't make sense to third parties to make games PS2 exclusive anymore.

The OG Xbox is one of my least favorite consoles of all time because I hate the controller, and Gamecube was my jam as a kid, but it's not hard to see why the console that was the only one at the time to get Doom 3 was considered more of a success than the console that never got a GTA or a Battlefront.

As other people have said, this one is a no-brainer, it stablished the brand, thats all. That in itself was huge. That it sold half the units they expected is secondary to having a firm foot in the market. Whereas GC sold even less than the OG Xbox and failed to turn around the brand after the low sales of the N64.

Sure, but those are outliers.  We shouldn't use outliers as a baseline for expectations.  Sega, NEC, SNK, Phillips, Apple/Bandai, Commodore, Panasonic, Mattel, Magnavox, Google (streaming) Steambox, etc first consoles were not that successful.  

Xbox established a brand, GC made people question if Nintendo should go third party (which was stupid IMO, but did exist).  Consoles went on to have HDDs are standard and online become a thing.  And PC ports become normal (when they were not previously).  The xbox had an impact, the GC didn't (from a hardware perspective).  Nobody uses z-buttons, c-sticks or mini disks.  

Edit

Apple has been trying to break into gaming as well, so far very limited success.  The OG xbox breaking into gaming is by default a success.

Microsoft carved a niche in a very competitive market. Nintendo ended up third on sales regardless of they being the oldest player between the big platform holders.

Funnily enough, the Master System, Sega's first global console, secured a bigger marketshare than the OG Xbox, the market itself was just much smaller then.

Xbox definitely had a big influence on gaming, arguably more so than even the PS2 despite selling a 6th as much. I guess I see success in more commercial terms, like did it achieve its sales goals; MS's aim wasn't just to establish a small presence in the living room, they wanted to establish a big presence and sell 50m consoles, and they didn't manage to achieve that.

It’s kind of like how one NFL team can have an 8-9 season and it’s seen as a success and another (probably Cowboys) can have an 8-9 season and it’s a failure. It’s all about expectations.

IIRC, original goal of XBOX at the time was to prevent Sony from making their devices dominating living room, since MS considered PS2 as threat to their business of personal computing. In that regard, XBOX was a success for MS.

In that regard, I would contend that Xbox actually failed as it did not prevent the PS2 from dominating the living room.

Microsoft took a risk jumping into a foreign market, and they topped Nintendo and Sega in their first swing. With PS2 roaring as it was, it shouldn’t be hard to see why Xbox OG is viewed as having been far more successful than GCN. Short-term financial data and raw consoles sales figures are not the end-all-be-all gauge for measuring success.

I'd say that OG XBOX stopped Sony from having monopoly in that market, gave alternative platform to devs (especially PC devs) and set the stage for both 360 and the way how consoles are designed in the future (as PCs in the box). So, from my POV, it did its job fairly well.