A belt drive uses a pulley with cogs that mate to teeth on the belt. A belt is made of rubber or other synthetic materials. A chain drive has sprockets with teeth that mate to the metal links on the chain. A chain is made of metal.
Belt drives require less frequent adjustments than do chains. Belts are quieter, run more smoothly, last longer and are cleaner than chains. It is also easy to tell if a belt is worn, damaged or needs to be replaced.
Belts can break and wear faster than do links on chain drives. Belts can slip (unless the belt has teeth) and snap during extreme riding.
Chains are stronger than belts and easier to repair. Chain drives also make it easy to change gear ratios by removing links. Chains are a better choice for high-torque applications and heavy riding.
Chain drives do not operate as smoothly as belt drives. Chains require regular lubrication, can kink and can cause performance problems if the chain is too loose.
Generally, dirt bikes, dual-purpose bikes and sport bikes come with chain drives. Many cruising bikes have belt drives. The best choice depends on the type of bike you want and the type of riding you plan to do.