If you process your own film, an attraction of 220 is that you can process twice as much in the same number of reels as 120, without having to try loading two 120 rolls on the same reel (which some people do regularly, but I prefer not to). If you're shooting a lot, 220 requires half as many reloads, making it particularly popular for medium-format wedding shooters. Zeiss also claimed that without the backing paper, 220 could potentially give better film flatness than 120, though I think you would have to be working under very tightly controlled circumstances to see it.
That said, if the film you want isn't available in 220, then it doesn't matter, and you're better off selling the 24 backs while you can and purchasing 120 backs.