I've used Uber much more than Lyft, but I've had almost entirely positive experiences with both. Only one time did a Lyft driver cancel a trip on me after I waited 15mins and almost missed a flight. I reported the incident through the app and a $10 USD credit showed up instantly in my account with a friendly note from the rep.

At an airport, an Uber driver picked up my fare and then immediately canceled it which caused a $5 USD charge on my account. A quick report through the app rectified the situation in < 24hrs.

The Uber experience is so seamless across time-zones, countries, etc and directly integrates with Expensify. If Lyft expands more into Europe, I will definitely use them as well. I tend to use Lyft more in big US cities. Hailo is also quite popular in Europe. When traveling, I never take a regular taxi if I can help it. The one exception to this is Dublin, Ireland. Taxis are so ubiquitous and cheap that you can get one 24/7 from almost anywhere in city by just walking outside and putting your hand out.

For the ultimate in customer service and luxury, Blacklane is better than both. You pay a huge surcharge for it, but sometimes you need a pre-scheduled ride that is 100% reliable.