As a starting point i would take a relaxed day result as reference and check which of the two tracker-result comes closer to the theoretical base calory amount calculated online for your body.
This seems to be quite normal, however it is a bit difficult to point you in any direction as you did note state much information.
Generally and one of the easiest and most accurate ways to estimate the Kcal burned e.g. when running is "distance(km) x weight(Kg)". So if you run 10km and your weight is 79 kg, then you have burned 790 calories.
It is generally concidered that the burned calories counter is not affected to pac or HR-zone.
Having said that you could take look at:
http://tools.mydr.com.au/tools/calories-burned-calculator
Depending of result of the above then you know if Myzone or Garmin Connect have the "right" number.
Calculating burned calories based on heartrate is a rough estimation and probably myzone and Garmin use different algorithms.
At least for Garmin you have to adjust your heartrate zones properly.
The mentioned calculation for running is probably quite valid and accepted, nevertheless this is also an estimation and cannot include factors like the running ground (mud, snow, road), effectiveness of your running style, wind, climbs, etc.
As the determination of calories in food is also not very accurate and what you burn is depending on your individual digestion system, it is not possible to exactly calculate what you can eat vs. what you burn. Nevertheless the numbers are good enough to help loosing weight or keeping it constant.
I’ve been investigating the same issue. There always seems to be circa, 200 cal delta between Garmin result and Myzone result (Myzone always being higher calorie figure) I’ve tried to input as much data as possible into both apps (weight / height / stride length etc etc..) the Myzone calorie formula is available on their website. However, I cannot seem to find Garmin’s formula anywhere - I assume this is proprietary information, albeit why Myzone share theirs.
If the HR is being taken from the Myzone chest strap, for both Garmin and Myzone, my conclusion is that their calculations / algorithm must be different. I’ve come to the conclusion that unless I can access a calibrated EKG machine to get a comparative result, I’m go by the Garmin calorie result as it gives a lower calorie value between the two. That, and I find Garmin to be more user friendly
To my knowledge Garmin uses Firstbeat's algorithms for calorie calculation (they licensed the tech before, then bought Firstbeat):
www.firstbeat.com/.../
Also, since you are talking about calories burned during a workout, these might also be of help:
https://support.garmin.com/en-US/?faq=lkl4cwCLlK7ox362uGQEV7