TL;DR: It depends. Strava is Facebook for cyclists; many of your friends are already there. Ride with GPS is the serious geogeek/cyclist’s companion; it allows you to create and share your own routes. I keep both apps on my mobile device, but I use mostly Strava.
With the demise of Google My Tracks, I needed to select a replacement app with which to track and record my bike rides on my Android phone. (I briefly considered getting a dedicated bike computer (e.g., a Garmin), which many veteran cyclists swear by. But the thought of owning and charging and managing yet another device quickly rendered this option untenable.)
On January 30, 2016 — the day of the Google My Tracks deprecation announcement — I went back to Strava, which I had signed up for years ago and subsequently replaced with My Tracks. The reasons I ditched Strava in the first place are still there today — it has way too much stuff. Challenges, badges, game-like “social” features are to me bloatware that I don’t need. But I kept using Strava, because it did what I needed — kept track of my rides.
Then I signed up for a charity 40-mile ride, which published the routes in what the organizers called “Garmin” and “Ride with GPS” formats. Garmin not being an option I was willing to consider, I looked at the “Ride with GPS” format, which turned out to be a GPX file. Can you import a GPX file into Strava? No. So I signed up for Ride with GPS.
I paid $2 for a three-day pass, I downloaded the Tour de Franklin route to my device, and I set out to test the navigation capabilities of Ride with GPS — in my car. Which is where I ran into problems (almost certainly attributable to my aging device). I couldn’t get the audio or spoken alerts to work no matter how many things I tried, and towards the end of the test — after about an hour and a half of driving — my device’s battery was at less than 10%. It was now clear that I wouldn’t be able to use Ride with GPS with my current device (Google Nexus 4) to navigate along a four-hour ride.
Back to The Google. After some digging I found a beta script on Strava Labs that allows users to upload a GPX file and convert it to an editable Strava route. At the time of this writing the script does not create new geometry data in Strava, only best-matches GPX data to geometry that is already in Strava. This was close enough in my use case, and my experiment ended. Strava won this round, if for the wrong reasons.
CONCLUSION: If I had to make the switch away from Google My Tracks today, knowing what I know now, I would select Ride with GPS. It is an excellent app with serious mapping chops.