안녕히 계세요 when YOU LEAVE (계시다 = 있다 = to stay → "Stay in peace") 안녕히 가세요 when THE OTHER PERSON LEAVES (가다 = to go → "Go in peace")

yes, usually like Hyejeong said. Guests say 안녕히 계세요 when they leave. Hosts say 안녕히 가세요 when guests leave. Happy new year

It's not a matter of what's more commonly used - they're both used equally. It just depends on the situation.