Thats a really good question. I don't think that their is a one answer fits all either. Different cars have different characteristics.
I think the main fundamental difference is they don't deteriorate with age unlike a belt which has a maximum time limit and their life is considered less that a chain. Belts are generally perceived as a consumable item that needs replacing whereas a chain may last the life of the engine, although the life of a chain is dramatically affected by the quality and service life of the engine oil. So chains generally wear and stretch with poor lubrication,they also have tensioning devices which can wear and need periodic replacement, but unless the service schedule requires, the car has been well maintained and their is no noise from the chain then you normally would consider it is ok and doesn't need replacing.
hope that sort of answers your question. Richy