If the Nintendo 64 used the same kind of discs as the GameCube, it would have been an incredibly advanced system as that kind of technology didn't really exist yet. If it just used a "mini" version of CDs, it would have had the same problem that the N64 had: not enough storage space.
If the question is about the N64 using CDs, there are a lot of variables to consider. The system likely would have garnered more third-party support, and the sales would be closer to the PlayStation. I still think the PlayStation would be the market leader, as a large reason third-parties jumped ship was due to Nintendo's controlling ways, something using CDs wouldn't really fix.
The big thing to consider though, is that Nintendo's design philosophy is what lead them to stick with cartridges. If Nintendo had released a CD system in place of the N64, they'd be a completely different company than what they were at the time. All of the N64's greats would be completely different games, and there's no way to know if that means they'd be better or worse. Personally, I find the N64 to be home to some truly excellent games, and I wouldn't want to risk them not existing by changing the N64 into a CD system.
I actually like this generation because the systems were so different, each system offered different experiences. Last generation (PS2, GCN, Xbox, Dreamcast), all the systems seemed the same, there weren't really any types of games that would be better on one system over another. Even this generation, the Xbox 360 and PS3 seem interchangeable. It's nice when systems have more reason to exist beyond just different games available.