Chains are fitted during manufacturing and are generally a "fit and forget" for hopefully the life of the engine. Chain replacement can be expensive depending on the particular engine design. In the Hilman Imp engine (Coventry Climax engine based) then the chain is easily replaced by opening up the existing chain, attatching the new to to old and then hand cycling the engine to thread the new chain through.
On other engines the chain and drives can be buried deep within the block.
Cam belts are generally cheap and very efficient. They are also very suited to high RPM applications and have less mass implications. They do however require routine replacement. Belt replacement is normally very easy and straight forward. However in some engine/vehicle applications, such as the Fiat Coupe 20V & Marea 20V, there is little belt access because of the engine bay width and Fiat recommend engine removal to change the belt(s).
Belts and chains have their merits.