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I know Garmin gets its data from an inbuilt barometric altimeter, or something, so should be/IS more accurate
It's not really any more accurate, it's just a different number.
GPSes just don't do climbing calculation well enough for it to be anywhere near reliable. Even the barometric altimeter in Garmin's is fraught with absurdities.
(I went for a long run last weekend. When I got to the Thames my Garmin was claiming I was at -5m altitude, 3 hours of running along the tow path, and getting back to that exact same point, it has steadily climbed to 11m altitude.)
Here's some science: http://www.staff.city.ac.uk/~jwo/landserf/audax/elevation.html
Greenbank
Lukas
My biggest gripe with Strava: rides recorded using a Garmin usually have a higher average speed and greater recorded elevation than the same ride recorded using the smartphone app.
I understand why the speed might be different (assuming both based on GPS, no sensors), particularly on a commute/through town, because ten seconds pass before Auto-Pause does what it is supposed to (and this doesn't always work if it's cloudy/wet/congested, due to poor GPS signal)... But, I've always envied friends' stats at the end of a week where we've ridden together; I look like the wimp who only rides on the flat (although, in/around Manchester, this isn't difficult).
Example: 14km morning commute when plotted in Route Planner estimates 57m or elevation, but the Strava records zero.
The same route in reverse, in the evening, allegedly rises 101m, but the app only records around 50m.
I know Garmin gets its data from an inbuilt barometric altimeter, or something, so should be/IS more accurate, but I feel aggreived at the prospect of having to pay Garmin Tax for that extra performance.