Your calculation for RMS power is correct. I'd be inclined to say that you have a fewer number of samples than Apple does, or something similar, and that would explain the difference. You can check by inputting a loud sine wave, and checking that Apple (and you) calculate RMS power at 1/sqrt(2).
Unless there's a good reason, I would use Apple's power calculations. I've used them, and they seem good to me. Additionally, generally you don't want RMS power, you want RMS power as decibels, or use the kAudioQueueProperty_CurrentLevelMeterDB
constant. (This depends on if you're trying to build an audio meter, or truly display the audio power)