Not more accurate, just different; and not a Strava vs MapMyRide distinction. Strava does offer you the choice of over-riding your Garmin elevation data and using the terrain data if you want to... like when the altitude record is whack from barometric changes during your ride.

Strava's not good for making maps, but it's real good at keeping track of your rides. They like to play up the competitive angle but you don't have to go there at all if you don't want to, and the free version has all the stuff I want.