Gamecube was quite memory-limited both in main and video RAM compared to XBox and PS2. My team was not the only one that had to play tricks to fit on that thing, swapping in and out parts of main memory (to/from the overly spacious audio memory area IIRC).

> Gamecube was quite memory-limited both in main and video RAM

I'm not saying it was a supreme machine without limitation, I'm saying it was the most powerful one. It had by a fairly large margin the most powerful CPU and GPU subsystems.

That doesn't mean there were no tradeoffs, it was all strength and it was necessarily trivial to make use of that power. Think PS3.

IIRC the Xbox was the most powerful console of that generation.

XBox was comfortably more powerful than the GC, GC was ahead but more similar to PS2 in practice, both were well ahead of the Dreamcast (Dreamcast launched first, PS2 next, XBox and GC last, so kinda to be expected). GC was hamstrung by memory issues (PS2 had better bandwidth, fill rate, media capacity, iirc), so was a bugger to use its power, but that's by the by.

So, I disagree with the first claim in your second paragraph, but my pedantry only supports your main point: PS2 won, selling 3 times the others put together. But PS2 was a long way from being the most powerful.

But, both as a developer and player, and purely subjectively, I do think XBox was the 'best' of that generation.

> The GC was the most powerful console of its generation,

That's not true. The Xbox was far more powerful CPU/GPU-wise, and had far more storage (the 8 GB HD was pretty amazing) so games could install themselves to HD and use virtual memory to increase their performance.