I like to separate your question into 2 sub-questions:
#1 How do we determine which side to charge?
#2 How much is the right amount to charge?

On #1, my answer is that you can charge the side(s) for whom you add the most value. In your examples, Uber really solves a big problem for drivers, it's that they sit idle for a good part of the day, so are willing to pay a lot for new leads. (their alternative is no work) Consumers are charged more for the convenience of a private car but they are probably not so much willing to pay more for a taxi, even if they can hail one from their phones.
For AirBnB, it's a mix, it's a way for landlords to monetize idle capacity which they are willing to pay for, but it's also a way for a renter to pay less than they would normally pay for a hotel.

On #2 (how much), I like to triangulate a number of factors:
- What's the maximum amount I can charge one side, while still being a good deal for them.
- How much do I need to charge so that I can become profitable? (the economics are quite different if you charge 3% vs. 12%)
- What are comparable services charging for substitutes/competitive offerings?

I will just add that there is no formulaic way to determine pricing strategies (curated vs. open), and it's a lot more about what's the comparable and what the value delivered is.

That's how I approached the question while deciding the business model at ProBueno.com (my startup)