Airbnb has more places because Airbnb has more people because Airbnb has more places (and so on). It's basically the same moat as Facebook. It works better than Uber, I think, because Airbnb is much more travel-oriented so it's hard to have a local competitor (who wants to install an app for every city you visit?)

VRBO can theoretically compete by being cheaper but comparison shopping between apps is a pain (there's no kayak or google maps aggregator).