Considering the PlayStation basically shaped modern gaming, things would be VEEEEEEEERY different.
Just take a look at the biggest games of each systems: FFVII, MGS and Tomb Raider on one side. Super Mario 64, Banjo-Kazooie and Ocarina of Time on the other. It's like night and day, and it clearly demonstrates how gaming would be without Sony.
Now, if Nintendo still dropped the SNES CD, but Sony's CEO just said "fuck this" and never released a console... well... the N64 would still be using cartridges. The Saturn would still be a mess of a hardware. Third-party games are mostly released on the N64, but they are far limited by the small capacity of carts. Final Fantasy VII would be an EXTREMELY different game for example, and probably would have not caused JRPG's popularity in the West.
Fast forward to the GameCube. It's likely Nintendo would go for optical media because of natural evolution. Jesus, in 2001 you can't stay with cartridges. The Dreamcast would have a strong launch as in this universe, but there would be no PS2 to make DC's sales plummet. Sega would survive.
Now, the Xbox is a little more tricky. Microsoft entered the console race because gaming devs were abandoning PC to develop on consoles. That's largely thanks to the PS1. It's very likely that PC would still be the platform of choice - again, thanks to N64's cartridges. It would be a Nintendo vs. Sega market, and there would be no need for a complete change of philosophy inside Nintendo - therefore, no Wii. And without PS1 and PS2, there wouldn't be a single home console that reached the 100 million mark. The industry would be MUCH smaller. It'd never become mainstream, and would be viewed as "toys" like in the 16-bit era.
