A heart rate monitor is only going to give an accurate estimate of calories burned during cardio exercise, not strength training. So I would not recommend using one for strength exercises.
The tracker doesn't know how intense your strength training routine is, so it's difficult to compare 20 minutes of this kind of workout to 20 minutes of another. If you're doing a really challenging strength routine, I'd agree that you'll burn more. It's just very difficult to know how much more.
In the grand scheme of things, it probably won't have a big impact on your weight loss progress one way or the other, so I would just consider any extra calories burned to be a bonus to your weekly goals.
Hope that helps,
"You may have a fresh start any moment you choose, for this thing that we call "failure" is not the falling down but the staying down." Mary Pickford