I've seen these anecdotes one way or the other (pro/anti Uber/Lyft/whatever) and I think they're all pretty useless when trying to extrapolate to the broader population. One thing that is abundantly clear, at least in the US city where I live, is that Uber and Lyft are pushing hard for the same pool of drivers; many drivers drive for multiple ride share services. I'm extremely skeptical of "one company's drivers are better" stories given they're all largely the same drivers.
You can try Apple's Maps app. (Does Google Maps have it to?) There is a 'ride-share' choice (or some similar terminology) when choosing route methods, and selecting it presents both Uber and Lyft (if you have the apps installed) and side-by-side price comparisons with the ability to book right there. It should be noted that integration with the Maps app is handled by Lyft and Uber themselves - they can choose what values to present to the user.
