Well, Uber is taking a heavy beating in Europe (and thanks to our regulations, taxi service never has been as bad as in the US, so the market for "better taxis" isn't as large to begin with), and AirBnB already bows to regulator's pressure all over the world.
Uber competitors didn't exist in Europe before Uber did. You are talking about actual "sharing economy" like the french carsharing service but thats a very different thing.
Airbnb didn't really exist either you are talking about things like Novosol that functioned as a middle man apartment renter.
1. Uber competitors existed – although those were usually financed by the Taxi companies.
2. AirBnB competitors existed in the way that you could rent your apartment to others via such services. Renting out private apartments was standard for decades and centuries even.