Incidentally, my experience with Lyft here in Canada has been pretty dismal. On average pretty terrible drivers. I have a feeling Lyft is getting all the Uber rejects. If that's the case, this is going to derail Lyft's Canadian debut pretty badly. I wonder if this is a common problem when they come into an Uber-dominated market.
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.
I live in NYC, however I'm from Toronto and spent a couple of weeks there last month. I don't use Uber, don't have it on my phone and I was surprised to learn how new lyft is to Canada. The lyft drivers I experienced seemed really good, however, when I asked them about why they downloaded lyft, they consistently said it was because of the 30 day no commission take from lyft, but they had no loyalty to the company. One guy even said he plans to delete it and move back to Uber once the entry offer is expired.
My experience is with the other end, I have been querying Uber drivers about their feelings about a possible upcoming entry of Lyft in my province's market.
So far, on my small sample 10<n<15, it has been unanimous that they would adopt Lyft since they have a reputation among drivers of taking a smaller margin. Some of the drivers also told me that they plan to serve as drivers for both at the same time.
