The gap between thumb drives being released and being cost-size-quality competitive with Zip disks was only about 3 years.
I bought my first thumb drive, a 256 MB unit, in spring 2004 after my buddy introduced me. It cost me about the same as four 100 MB Iomega Zip Disks, IIRC.
The 100 MB Zip Disk was the most prolific size, as that was the initially released drive capacity; if you were carting Zip Disks around between different places, you couldn't be sure the drives elsewhere were the 250 MB version. My University had 250 MB Zip drives installed in most of their PCs (ca. 2003-2005), and that was the way I transferred schoolwork between my home computer and school, up to the point I bought a thumb drive. The 750 MB Zip drives were released around that same time, but they had an epic design shortcoming such that they were read-only for 100 MB disks (I found this out the hard way, after buying one). The 750 MB disks were priced too high to justify purchasing only for my drive at home (my home computer had a 160 GB hard drive, at that point).
Zip Disk also had an issue of failing pre-maturely in dusty environments; not a problem at the university, but we went through tons of Zip Disks in the Army, just a bit prior to my time at the university. Dust is not really a problem with thumb drives.
As a company, Iomega also had the Jazz Drive (which I never saw in-person), which started at 1 GB, and similarly went up a bit in capacity over time. Jazz Drives seemed to be mostly marketed for graphics and A/V profession editors. Iomega crashed just a couple years later (there was the 750 MB drive debacle, thumb drives outpacing their tech, and some other poor management decisions).