Max was released in 1996 and Maya in 1998. From my foggy recollection, it took a while for Max to become widespread so my hunch is that 3D Studio for DOS and Lightwave ruled the roost for most of the 90s.
As far as I remember, 3DSMax was still an outlier throughout the 90's, but it quickly gained popularity in the PC game development scene because it also ran on PC and didn't require a separate investment in SGI workstations or beefed up Amigas (and I guess the rampant software pirating on PC in the 90's also played a role to make 3DSMax popular).
https://en.wikipedia.org/wiki/Kinemation
BVH format is still floating around. The Biovision motion capture format. I am quite surprised!
No one could top Maya back then in terms of flame, water & particle effects: