I prefer Lyft over Uber, but Uber has better international coverage. Typical wait time is ~10 minutes. While they are both usually a bit cheaper than a taxi, I find the vehicle tracking part of the app very useful for knowing how close are they to arriving, as well as keeping an eye on the route used between origin and destination - esp when in a foreign city and not really knowing the area - you can at least see that they're going in the right direction. They both use a demand-based pricing model, and charge extra fees for certain sources & destinations, like the airport.
Downsides:
1) You have no clue who is picking you up. Uber does very little in terms of background checks. This is basically organized, paid hitchhiking to a certain degree. I've had a couple 'interesting' drivers, and while the ride worked out in the end, I was questioning my decision making skills during the rides.
2) It can be hard to spot your ride, especially if they're picking you up at busy location like airport arrivals, since it's just a normal car. You basically have to play 'spot the license plate'.
3) I also have some personal 'religion' issues in that I won't ride in certain brands of vehicles, ever, and there's no way to specify those preferences in the app. I just cancel the ride if I have an issue, if there's a cancellation fee to do so, so be it.
