I know they say belts are quieter, but I hear belts when I don't hear chains, especially the Hy-Vo or "silent" type chains. Belts are usually under a thin plastic cover, and I can usually hear their high-pitched whine. Not really loud, but definitely there. Standard type chains are lower pitched, more of a buzzing sound.
Another advantage of chains is they are narrower, allowing the engine to be a little shorter. But I like them mainly because they are reliable and long-lasting.