I had the chain changed on a mid-seventies Peguet 404, and on an early eighties Alfa Romeo.
The 404 chain became noisy, and to replace it the front timing cover had to come off.
On the Alfa DOHC engine, the chain was replaced as pre-emptive measure, and the replacement procedure did not involve removal of the timing cover - instead it involved removing the camcover to expose the cam sprockets and the top of the chain, then rotating the engine till the link in the chain was accessible, open the link, loosen the chain, connect new chain to old chain and pull it through... then refit properly and tension, recheck timing and secure camcover. The chain on the Alfa was also a double-row chain making total failure (of the chain - not the tensioner...) less likely.
Both jobs were neither difficult or particularly time consuming.
But the belt on the 1.8 Mk1 Astra was really a doodle, it would simply slide-off and the new one slide back on with no timing issues...
On balance I think that belt driven engines are cheaper to produce, and yes they may also be quieter, but chains are in my opinion better because they are more likely to give some early sign of trouble i.e. noisy operation before giving up the ghost, where as belts notoriously just go.