Given the PS2 had Ridge Racer 5, SSX, TimeSplitters and Tekken Tag at launch then games like ICO, Silent Hill 2 and Onimusha in its first year I think you couldn't be more wrong.
Eh, it's all relative, and price/library massively favoured the Dreamcast for that year.. not that it even mattered, because the PS2 had killed the DC before it even hit the shelves. Whilst I fucking
love Ridge Racer V (best in the series by a wide margin), it was very much seen as a step-back for the series at the time, and Tekken Tag was viewed as a very conservative semi-sequel to Tekken 3, and certainly wasn't being compared favourably with Soul Calibur at the time.
But OG XBox didn't dent PS2 somehow. The PS1 momentum probably mattered to devs.
Momentum, yes... but that momentum snowballed when the PS2 specs were revealed, along with those famous tech demos (Reiko, Old Man, etc), it cuts the legs out from under the Dreamcast almost immediately (which had been gaining quite a bit of momentum before it suddenly became the "weak" console.
The OG Xbox doesn't really factor into this, because it simply arrived on the scene too late to even factor. The PS2 launched with the hype of being a super computer at home, and the most capable games playing device there was. If the Xbox had been revealed early enough to undermine the PS2's hardware prowess (like the PS2 did to DC), then it probably would have made a far more significant dent... but it didn't.
Also, I want to be clear that I'm not saying that console power is the alpha and omega in terms of how a generation plays out (we have more than enough examples to contradict this). I'm just pointing out an example where I recall the mere allusion to the power of a system being able to but the breaks on a competing platform.