Nintendo probably would of became a juggernaut of console gaming if this had their deal with Sony gone through. Who could of really competed against a partnership that would of likely also led to a "Playstation 64" if you will where both the best of N64 and PS1 all on one system. There would still be companies who try, but no one could of possibly made something quick enough to what would of combined two consoles that still hold a huge influence on today's gaming world.
Also if Smash Bros. still came out. Spyro, Crash, as well probably Final Fantasy characters (Both old like Black Mage and new at the time like Cloud) would of definitely been part of the roster at least when it got to the time to make Melee for the "Playstation Cube".
Of course that's just assuming most of what happened still came to be. It's impossible to really know what would what would happen to everything that we know came after. But we can take guess a Nintendo-Sony partnership would be like monopolizing the entire gaming market at the time cause the only major competitor at that time was Sega who was already (or at least going to be) reeling from the failure of the Sega Saturn pretty much.
There's two ways of looking at it if you're a pure Nintendo fan this would mean Nintendo would dominate the console market for many years to come. But if you're a multi-console owner or someone who wasn't into Nintendo then you're alienated because any other consoles even if they do fairly well at first just aren't going to compete well. It all defends if you prefer a healthy competition of companies so each one raise the stakes and pressure the other on making bigger and better games or if you'd just like a single company having near ownership of the entire industry. Some of the important games made during the era of the PS1/N64/Dreamcast were partly made because they were attempts to make games that could compete with others within the market. If there's no pressure on a company to make a great game that rivals a competitor's then a company may feel they can get away with just about anything, including games of significantly lower quality then it could be (Although sometimes that happens anyway even in a highly competitive market, but it'd be even worse if it's just one single company that owns the market.)
So while yes, the partnership would of given Nintendo huge control. It'd also be bad because some of those games you loved either may have not been made at all or they could of not been quite as good as they tuned out to be when the companies had to make sure their game was good in comparison to a competitor's game. It really wouldn't have been good from an entire industry perspective. But if you definitely look at it from Nintendo's point of view, it was for sure a missed oppurtunity to claim pretty much total control of the market.
I'm not saying Nintendo with Sony would lose it's quality control that fast. But once it was obvious they were dominating the market though, they could of gone quite laid back.