To build on what I said earlier, it would be a battle of CD vs 3D. A weaker Saturn would still have been a 2D powerhouse, and would have had all of those benefits of the CD-ROM. But the industry in general was largely pushing towards 3D graphics and gameplay, which was where the N64 was much better off.

I could easily see there ending up with a very strict demarcation by genre. So if you preferred 2D fighters, you'd basically have to get a Saturn, whereas for 3D platformers, it's be N64 or bust.

Saturn.
Cartridges screwed Nintendo over. They were too small and expensive.

Nintendo 64.

Nintendo was larger and more powerful than Sega by a massive margin. The N64's games were more expensive, but the system itself was much cheaper, and one of Sega's big problems was that they couldn't really consolidate the Saturn's components in a way that would facilitate aggessive pricing. They tried to mitigate it by packing games in with the Saturn to make it seem like a better value, but it ultimately didn't help.

Enix would have stuck by Nintendo - there was nothing in their games that really demanded CD-ROM storage, especially by the time Dragon Quest VII finally released. Even in the real world, DQ7 spent a lot of time in development hell on PS1. Enix supported the Game Boy/GBC in a big away at a time when Square had jumped ship to the WonderSwan.

Square might have just sucked it up and dealt with Nintendo, too, in the absence of a viable competitor, and worked around the cartridge format. It wouldn't have been the first time they did so. They originally planned Secret of Mana to be released on the Sony SNES CD-ROM add-on, and rather than move that project to the Sega CD, they just worked around the cartridge format of the SNES. Sega certainly wasn't in any position to give Square the kind of support they got from Sony.

Namco had tentatively begun mending its fences with Nintendo with games like Tales of Phantasia on SFC, and this might have been an opportunity for them to make peace. Eventually, they did become solid partners. As it was, they decided to go with a company that they didn't have a lot of prior baggage with, and they helped launch the PS1 to early success the way Pac-Man did with the Famicom a decade earlier. Maybe Tekken, Soul Edge, and Ridge Racer would end up being the N64's lead arcade titles instead of Killer Instinct and Cruis'n USA. Not to mention Tales of Destiny and Tales of Eternia. Namco was tentatively investigating bring the Tales series to the N64 (they eventually did bring Tales of Symphonia to the Gamecube, where it became the series' biggest hit up to that point). Fun fact: Even in the real world, Namco still released more games on N64 than on Saturn.

Konami, in our timeline, already supported Nintendo to a solid enough degree. That said, I do think that MGS would have ended up on Sega Saturn. Kojima did have history with Sega with Policenauts and Snatcher.

Capcom is a bit of a question mark. They might have supported Sega more strongly. They were already putting SFA and Marvel fighting games on Saturn and taking advantage of the 4MB RAM expansion. Would they have gone all in on Resident Evil on Saturn? They did manage to get RE2 released on N64. 

Sega itself still had a lot of problems with infighting between its various divisions that contributed to the Saturn's issues with hardware and marketing, and these had nothing to do with either Sony or Nintendo. Those issues contributed quite a bit to the poor perception of the Saturn outside of Japan. People were distrustful of Sega after the way they handled the Sega CD, 32X, and the Saturn. Nintendo, at least, had a clear vision of what they wanted to happen.  Sega also misjudged the market. They thought people wanted prettier versions of the games that were hits on SNES and Genesis, and that's what the Saturn was geared towards. 3-D was an afterthought for the Saturn where it was the driving force behind the N64, even moreso than the PS1. I'm sorry, but X-Men vs. Street Fighter was never going to beat Super Mario 64 in the marketplace. 

And then there's Nintendo's first party plus Rare's output, which still carried the N64 to 32 million units against the PS1's formidable third party arsenal and with only Konami and a few mid-sized Western developers supporting the N64. Globally, the N64 outsold the Saturn at roughly 3.5:1.  Mario, Zelda, and Goldeneye alone might have strengthened Nintendo's position in a world where their only major competitor was Sega. Sega simply didn't have the kind of first-party lineup Nintendo did.

I don't know if the N64 would have sold 105m units in this scenario, and that's as much down to the fact that Sony did think bigger during this generation as far as a mass market for gaming,, but I do think Nintendo would have won out over Sega by a comfortable margin.

This is a really good point that I admit I didn't consider myself, that the Saturn itself would be different if not for them feeling threatened by PS1.

Would have resulted in a gen where N64 had a huge advantage in terms of 3D rendering, which in an era where 3D was all the rage, may have given Nintendo's system a major draw.