It would have stayed more of a "Sega vs. Nintendo" market, at least for a little while. Sega would have done things differently with the Saturn if it hadn't been for Sony. For one, the Saturn was originally going to be quite a different machine than what it became, but Sega changed it in response to the design of the Playstation. Had Sony never entered the market, perhaps Square wouldn't have jumped ship and Final Fantasy VII would have been a Nintendo 64 title, as originally planned. Basically, everything would worked out very differently.
Here's some more info:
"Seeing the Sony threat on the horizon like a polygonal T-Rex (which is probably the demo that scared Sega execs in the first place), Sega changed the design of the Saturn. Not by creating a dedicated 3D machine. No, it added a second processor to work alongside that magnificent 2D circuitry. The result, in theory, was an even more powerful machine. But in practice, this unusually complex architecture was disastrous. It was just too difficult to get good results for the majority of developers."
http://www.gamesradar.com/sega-saturn-turns-20-its-not-shit-as-you-think/