Looking at the material form which both are made of let us know that chain are made of alloys while the belt are made up of polymers
Talking about the working condition chain drive can work in high temperature and moist conditions where as belt drive need dry condition to work properly
Because of the slippage efficiency of the belts drive is very less as compared to that of chain drive
Because of the metal to metal contact in chain drives they very are noisy but in belt derive no metal to metal contact so no noise at all
Speciality of Chain drive is that it can operate under high loads while belt drives Speciality is that it can operate under high speed conditions.
Chain drive have high initial cost and also need lubrication with time but last long that belt. On the other hand belt drive have low initial cost but it wear soon so need to repair regularly. Belt drive do not need lubrication