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Neither were based on HR. My profile on Strava is setup with my sex, DoB, max heart rate and weight (80kg). The same data is stored on my Garmin with the exception of DoB. I actually recorded the latest ride on both devices (via the Strava app on my new phone) to allow me to compare. The distances match to within 100m (over 50km), average speeds are slightly different (24.2km/h on the phone, 23.7km/h on the Garmin), which seems to be due a discrepancy in the total moving time, which I'm guessing is due to different auto-pause algorithms.
@PhilDAS the energy expended is returned in "Calories", which I think is the non-technical way that KCal get reported. When I look at the activity on my Garmin it says 1978Cal for that activity, which is pretty consistent with all the previous rides of this route (i.e., my history on Strava) recorded through it. So I'm guessing that when the Garmin is used it calculates the energy expended itself and this value gets imported into Strava with the other ride info (which I do by transferring the file from Garmin to laptop and then uploading to Strava); the new value of 1,011 calories, on the other hand, appears to be the result of Strava's own calculation. What I can't work out is why there's such a massive discrepancy. Annoyingly cycling calorie calculators like this seem to come up with a value almost exactly halfway in between (1,500 Calories).
Calories guesstimated by different devices. They're gonna be using different equations. Were they both off HR? Do you have weight accurate in both? Basically I would ignore any calorie estimations that aren't based off a PM.