Basically, significantly heavier and more friction loss than chain drives, which is why Orville and Wilbur use chains to drive their propellers. Advantages can be long life, low maintenance, and not exposing mechanical hazards (pinching and cutting) and not subjecting the users and the immediate environment to oil and grease. Chains drives can be fully enclosed, which falls somewhere between in features/benefits.

There are also belt drives with their pros and cons.

Note all four setups have been used on various motorcycles and scooters since the 1920s... belts no so much as it wasn't until relatively recently that they were made strong and reliable enough.