It is possible you are comparing apples to oranges. The “Workout” app reports active calories burned. The “Activity” app displays both the active and resting calories burned during the workout. The total calories burned during the workout will include both the resting and active calories. It's likely that the other devices you used include both. I assume the 690 calories you report are just the Active calories.
One example: I walked a 5.1 mile route at 4.3 mph and the workout app says I have burned 451 calories, but the Activity app also includes 130 calories of resting, for a total of 581 calories. I used an online calculator that uses my height, weight and age and it estimates I should burn 517 calories. The online calculator doesn’t use my heart rate or the elevation change during the walk, so it should be less accurate. The walk has an elevation gain of 600’, so it is logical that my calorie burn should be more than the online calculator. The watch appears to be fairly accurate in this example.
I have made this same walk four times using the watch and it has been within 6 calories each time… very precise! My walking speed ranged from 4.1 to 4.3 mph on the four walks. I also have made two 6.3 mile hikes (with a 1300’ elevation change) and the watch calculated a total (resting plus active) of 850 and 828 calories (also quite close). The 850 burn was at a faster pace with a 128 bpm heart rate, compared to 115 bpm for the lower calorie burn, so the difference in the calories seems about right.
I put your statistics in the same calculator and it estimated a 966 calorie burn for your run (again, no heart rate info). I assume the 690 calories you report are just the Active calories, so that would require 276 resting calories to make up the difference. I am about the same height/weight as you and my resting calories for an hour would be a little over 100 calories, so 276 seems a little high. However, I am over 20 years older than you with a 50 bpm resting heart rate, so your resting calories would likely be higher due to your younger age (and possibly a higher resting heart rate). Given all this, I would say the watch may be slightly low in your case (assuming the online calculator is accurate), but the watch still seems more accurate than the other devices (assuming the 690 is only the active calories).
The only other thing that seems odd is the heart rate during the run… it seems very high. Do you think it is accurate? Are you using the “Power Saving Mode” in the Workout app? You can check this on the Watch app (on the iPhone) and look under the Workout app settings. The Power Saving Mode still measures your heart rate, but is less accurate than the default mode.
The most accurate way to measure calorie burn requires measuring your oxygen consumption, which has a direct relationship to calories. The Watch/iPhone (and all your other devices) use indirect methods to estimate calories. In general, a device that use heart rate, distance and elevation should be better than a device that only counts steps. However, I don’t really care if the results are completely accurate, as long as they are consistent. I simply want to be able to compare one workout with another. The Apple Watch has proven to be VERY consistent in my experience so far.
Dave