The fundamental difference is in the material and construction. A chain consists of metal links connected by pins, while a belt is made of continuous carbon-fiber-reinforced polyurethane. This leads to different properties in practice.
In terms of durability, the belt wins convincingly. Whereas chains must be replaced regularly due to stretching and wear, a quality belt often lasts the entire life of the bicycle. There is also a clear difference in terms of noise: a belt functions almost silently, while a chain, even properly maintained, always produces some noise.
In terms of maintenance, there is no comparison: a chain requires regular cleaning and lubrication, while a belt requires hardly any maintenance. The weight is often slightly higher with a belt drive, but this difference is minimal and hardly noticed while cycling.
An important practical difference is resistance to external factors. A belt is completely immune to rust and much less sensitive to dirt and mud. As a result, its performance remains consistent, even under harsh conditions or intensive winter use.