Surprisingly (for me atleast), the xbox had the much more capable CPU, it wasnt even close (as compared to what the PS2 uses as CPU). During the 6th gen itself i thought the EE was the most powerfull cpu of the time.
NV2A was supposedly very far ahead aswell, in a different class alltogether if devs are to be believed, programmable pixel shaders and its twin vertex shaders, clocked at 233mhz, teamed to double the amount of quad pumped ram, it was quite 'unfair'.
The Xbox also had access to 1gb of HDD for 'scratchpad', hardware dd5.1 (all games have it, basically).
I'd forgotten about the Xbox sound chip! Yeah, it was quite a beast for its time iirc (just checked, and yeah DD5.1 encoding, 256 stereo voices, 64 3D channels). It was so good and so underutilised that I'm sure I read that MS decided go with something simpler and cheaper for X360, and lean on the CPU to do more of the work that time.
I remember ERP (i think it was him) saying that regarding multiplat games, they had the PS2 as a baseline, and the xbox was just porting and it would work quite well.
I think he also said something to the effect that PC / Xbox versions would have increasingly had more effort put into them as the GPU landscape shifted, and I think he was implying that the PS2 would increasingly struggle to keep up where this was the case. Which makes sense I guess. When an increasing part of what makes your game look good is Z-brush bump mapped models, high res textures and pixel shader effects, a system that's not adept at these things would comparatively suffer.
The PS2 was very impressive for its time of japan-release (march 2000). The Xbox with its november ww 2001 release was even more so impressive though. The GC was supposedly trading blows with the PS2 in many regards, to contrary belief it was doing that with the xbox. Probably due to it being released around the Xbox's launch.
Early on I think the GC made quite a splash - pretty good geometry, some nice lighting effects, and colourful textures. PS2 never really had satisfying textures (IMO and I acknowledge others will feel differently), but in many other ways the complex but fast PS2 hardware had room for growth as the industry developed its knowledge and experience. Being unquestionably the number 1 platform magnified this effect IMO.