PS1 and PS2 were weaker than their main rivals.
The difference being gaming is no longer a hobbyist market.
PS2 was the weakest of it's generation though, and won handily.
PS2 and PS1 were not the weakest of their generations.
And if the implication is that Sony didn't pursue a 'power angle' in those generations, nothing could be further from the truth.
Hardware superiority was present at both systems' launches, and was a factor to one degree or another in their success. Playstation's hardware left Sega reeling with Saturn. PS2's hardware did nothing to help Dreamcast. Microsoft dithered on launching a system in 2000 because they felt they couldn't outgun PS2 by any notable margin (and thus would have probably had a much harder time establishing a foothold).
That in both generations other competitors later arrived with more powerful hardware simply reflects the improvement of tech over time - not a decreased appreciation at Sony of hardware and power in those generations.
Every generation needs new, differentiated entertainment experiences that are valued by the market. Every generation PS has been present in, bar one (the parallel 'Wii' generation, if you like), has fueled that new entertainment via performance and hardware improvements. Sony put out the best machines they could each gen and hit the sweetspot in 2 out of 3.
Sony's philosophy on hardware was crystallized by PS2, IMO. The same philosophy that built PS2 built PS3. The 'only' change was in the budgetary constraints SCE was operating under as a growing sense of invincibility established itself.
I think it is pretty safe to say that sense of invincibility is no longer present though.