PS1 still wins the gen but not by as huge a margin. Sony as a parent company already had the global market penetration to take Playstation to levels Nintendo wouldn't have been able to at the time. Playstation also treated 3rd party developers much better than Nintendo and would've probably still secured a majority of 3rd party games. The only exception being Square.
And that one exception literally made all the difference in Japan, and by extension, the United States, since the US game market was still dominated by Japanese games at the time.