I think the biggest similarity is consumer mindshare and the art of turning your brand into a verb.
Even if I'm ordering a Lyft, in conversation I'll say I'm "ubering".
Likewise when booking an "AirBnB", I'll browse all sorts of alternative sites just to spot check locations/prices/etc.
The real limit to the market is how many players are in the game.
Remember when Austin Texas had a fingerprinting law that prevented Uber/Lyft from operating inside the city? There were a million and one alternative services, but generally both drivers and riders would recommend and use one or two based on personal experience/word of mouth recommendations. (ie- Ride with a driver that provides a good experience and who talks about which ones he or she uses and likes, then you will tend towards those apps rather than the smattering of others)
In markets like these where both the buyer and seller are using a 3rd party to accomplish a secured transaction, there seems to be only room for a few. This generally is down to mindshare of both the buyers and sellers, which comes down to marketing and getting your name out there.
Uber and AirBnB are in the same boat. They have the market's mindshare and brand name recognition... and thats about it.