I frequently run both Strava and RideWithGPS on my android device. But they have different features.

RWGPS locks the routes for "free" users so they are unusable.
RWGPS, however, displays current speed and current climbing data (with cumulative climbing 2x or 3x higher than Strava).
RWGPS handlebar mode is nice, allowing viewing data without the finger swipe. For power savings, on long rides, I set my phone to 15 seconds or 30 seconds, so one button to display data, then let the screen time-out. For shorter rides, I use a downloadable utility called NoScreenOff to keep the screen active.

Strava routes are functional (although if running offline, be careful about exiting and re-entering).
Strava post ride analysis is nice.
Strava segments and data sharing are fun.
Unfortunately, Strava only displays average speed + distance.

On a recent mini-tour, I kept a running log under RWGPS, and daily activities under Strava.