If CD vs. cartridge were the biggest reason why the PS1 won vs. the N64, then explain the Saturn.
PS1 was easier to program and was more powerful in the 3D department then the Saturn. Plus throw in the whole 32X and SEGACD thing and alot of consumers lost faith in Sega. You said that "During the first year the Playstation and Saturn sold almost equally" and this is true. But that was before FFVII was released. That game alone sold millions of PS1's.
Don't forget that Square was making the game for the N64 before jumping ship to Sony. I believe that if FFVII and the rest of the classic Square library made it to the N64 and not the PS1, the N64 would have dominated.
You seem to base the PS1's success on the release of FFVII (ports of NES and SNES games were hardly a reason for anyone to own a PS1). Remember, the PS1 outsold the N64 by 3:1 over its whole lifetime, a difference of about 70m consoles. No single game alone accounts for the success of a console and let's not forget that the N64 had games that sold more than FFVII. The PS1 had already won before FFVII was released.
If you believe that FFVII was the reason why the PS1 succeded, do you also think that FFXIII is going to turn around the fortunes this generation?
Other things to think about: Why was the Saturn destroyed by the N64, if CDs were so superior? Why did the company with the weakest 1st party games win the 5th generation by a landslide? How come that 3rd parties abandoned Nintendo and Sega long before the Playstation was in an absolute dominant position?
Really, the change of the business model was by far the biggest factor back then in the 5th generation. Nintendo and Sega were left behind with their old policies, while Sony allowed everyone to make as many games as they wanted. This resulted in a huge library with a lot of variety and gamers flocked to the Playstation because there were so many games to choose from.
It didn't matter that the majority of the games were bad as long as there were enough good games. The same was true for the PS2 and the same will be true for the Wii. A console is only in trouble when there aren't enough good games. Now I should quantify how much is enough: I say that ten good games per year is enough for the majority of gamers, most gamers buy less than 10 games per year.