Originally Posted by nhluhr

This doesn't make any sense. Both RWGPS and map data are using DEM data for elevation, probably the 30-ft resolution version if you're in the USA.

The answer to OP's question is that Strava selectively filters out small elevation changes to smooth the data (to avoid the "Richardson Effect" jmX mentioned). DEM will often NOT have accurate data for roads but rather simple low-res topographic data which doesn't account for roads cutting through hills, bridges, etc. Also, RWGPS uses very little smoothing in their calculation.