Cost
Compound light microscopes are generally more common in classrooms due to their relatively lower cost. As low as a few hundred dollars can purchase a compound light microscope; however, many more advanced models can cost well over $1,000. Stereoscopes -- although not too much more -- still have a higher price tag on average, often running closer to $1,000 for lower-end models.
Light Usage
Both types of microscopes have a relatively similar look and operation, as each one merely magnifies an object presented on a slide. A compound light microscope has a light below the specimen viewing platform, meaning it shines upwards, helping to eliminate the object. A stereoscope also has the below-platform lighting; however, additionally, it has lighting above the platform which shoots downward towards it. The goal is to help illuminate the object further and provide a more 3D look to the specimen.
Magnification
Compound light microscopes offer more power, but with less clarity than stereoscopes. Standard compound scopes generally have a cutoff magnification of 1,000X. Stereoscopes, on the other hand, usually have a much less powerful magnification, often maxing out at 400X.
Objects
With a different magnification comes a different set of objects which can be viewed. Many classrooms use microscopes when teaching lessons about cells because most cells are viewable under a standard classroom scope. Stereoscopes are limited in this capacity. Although they can view eukaryotic cells, they are still eluded by much smaller prokaryotic cells, which usually require a microscope that can at least zoom in to 600X. Compound light microscopes can easily magnify the adequate amount to view all cell types.