Final Fantasy VII almost single-handedly tilted the balance in favour of the PS1.
Not entirely true. In fact, Square was working with Sony before there was any idea of FFVII. Secret of Mana was supposed to come out for the SNES-CD addon, but due to reason known, the game had to be cut significantly to go on a regular SNES cartridge. There are sources that even say that this very experience is one of the if not the main reason why Square went along with Sony, after they broke off and made their own competing console. Square continued with Nintendo's SNES for a while because.. well.. it was the best selling console in Japan by far.
This was not just a format change that made Square switch, but a more business and cultural one. Both of them got fairly close as companies and Square didn't release any game (other than FF) for the N64.
Liberate Hong Kong, the revolution of our times!