I have done some research. It looks like yours is more accurate according to this calculator:
Walking Calorie Calculator - High accuracy calculation This calculation for a brisk walk burns 24 steps per calorie, using 2000 steps per mile. This means 396 calories for 9500 steps. This compares favorably with your 384 calories. My activity band is using, depending on its measure of effort, anywhere from 18 down to 12 steps per calorie. I need to see if I can fix this.