A powered output has the final power amplifier for driving the loudspeakers built-in so that it can cpnnect to passive speaker systems. The speaker connection on your home theatre receiver would be a powered output. An unpowered output does not include the power amplifier - it feeds line level to an active speaker system where it is further amplified by an internal power amplifier to drive the speakers proper.

Thanks, I was not familiar with those terms.

Unless there is a reason why synching in post is a problem, I'd suggest taking the transmitter out of the loop and record straight off the board with a digital audio recorder. Without having to go through the wireless transmitter you'll get better, more reliable audio, but the downside is you have to sync the audio in post. While voice recordings don't suffer much via wireless, a full range recording of a performace would suffer a little bit of a quality loss. Straight off the board is the way to go, if you can manage it.