It's never been the case.
The GC was the most powerful console of its generation, the PS2 was by far the least powerful one (with the possible exception of the Dreamcast, not quite sure where that one was).
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.
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.
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.