Calorie counting!

I'd run with the Strava data, as at least it will have made some attempt to incorporate the power output, even if that is also an estimate.

Agree with all the other comments that a power meter is really the only accurate way to tell, but there are a number of online calculators that take into account a lot of metrics including weight, bike weight, road conditions, tyre pressures, terrain, headwinds et cetera; I used them sometimes before I invested in a power meter and they certainly seem fairly accurate.

It will depend what metrics you have linked to your Strava?

If you've got a power meter and heart rate monitor then it's likely to be more accurate than the watch which, I presume, will just have heart rate.

That being said my Garmin head unit usually produces very different calorie figure to Strava despite both having the exact same inputs so I'd take any figure with a pinch of salt.

As you say, they're estimates based on an algorithm. But they can help if you are trying to lose weight by calorie counting, as on days when you've done a big ride, you will be able to eat more and still be in deficit! I have managed to lose weight a few times doing this, though it's a pain logging all your food intake! I've used both Fitbit and Apple Watch successfully to track calories - they seem to be ball-park accurate enough for this purpose. (I found this interesting article about it online)

One key thing to make sure is your weight is set accurately in the Strava app and also in the Apple Health app. This can have big effect on accuracy. Also, the use of a heart rate monitor (or power) will improve accuracy (obvs. the apple watch has HR built in). Did you use a bluetooth HR monitor to link to the Strava app?

I saw an apple promotional video a while back (can't find it online), where they explained the research they'd put into developing the calories burned algorithm. It did seem quite extensive and the Apple watch usually does quite well in reviews when compared to other similar devices.

Neither are likely to be very accurate in my opinion unless you are using a power meter and perhaps a heart rate monitor as well.