One big reason is that the PS3 was far too advanced for its time. Sony was taking a loss of a few hundred dollars each even with the $600 retail price. Given the price, and the fact that developers hadn't gotten used to the new architecture, it did not sell well initially. The PS2 still outsold the PS3 for quite a while.
Another is that Microsoft/IBM ripped off Sony's R&D for the XBox to get to market faster. The Cell processor was a joint venture between IBM, Toshiba and Sony who together invested hundreds of millions of dollars. Microsoft later came to IBM looking for a new CPU, and IBM used the Cell R&D to create the Xenon, which is basically a triple-core version of the Cell's PPE.
For the record, I have all three consoles, and the only console where I've bought a previous generation is the Nintendo, so there's no PlayStation loyalty going on here. IMHO, each has its strengths and weaknesses.
You clearly don't know what you're talking about on this. There is just too much wrong to even begin to correct.
But whatever the reason doesn't matter as the xbox made huge in-roads on the playstation and surpassed it. And if the PS3 was so far advanced why is the GPU weaker than the 360's? And why do most all the multiplatform games look best on the 360. I mean technology that is so far advanced should easily have better looking multiplatform games--just like the xbox over the PS2 last generation.
The real issue with the PS3 was that Sony wanted to get bluray on the market and wanted to use their playstation brand to achieve that. They did get the format on the market and bluray didn't fail as beta did; however, it really cost them another market--the gaming market. Which is more valuable? I'm not sure but with everything going digital distribution I think the long term win would be winning the living room.