I blame the PS1's success on the strength of it's games, not on its hardware. The sheer number of great games, as opposed to the number of great games on N64 or Saturn made it a winner.
I can think of one game that was really a great game, the game that made you buy the console, on N64, and that was Goldenye.
In comparison, with PS1, you had Gran Turismo, MGS, FFVII-IX, Rige Racer, NFS, and so on.
Saturn had....what the hell did saturn have that was worth buying the console for, anyway?