I've tried it on both - phone-app and Garmin, sometimes at the same time.

Strava ignores the Garmin's altitude reading (barometric altitude is way too inaccurate) and uses map points for those calculations.

I've found the 2 to be almost identical. I once had a 0.1 mile difference in a 34 mile ride, though the climbing feet were identical.

What I found interesting: The Strava summary was far more accurate than the Garmin showed while riding. I.e. Garmin showed inaccurate data while I was riding, as it was out of sync with a regular bike computer, with the phone app, and with Strava's eventual summary. The phone, computer, and Strava were all in synch, though.

I do - as do many of my riding buddies, and numerous people here on BF. See this thread:
http://www.bikeforums.net/showthread...-or-equivalent