Which one drain battery slower, airplay or hdmi?
Depending how scientific you want to go, the direct cable would normaly consume less power then wireless transfer.

That is true when using the correct cable (high quality) since the cables also have some resistance (power consumption) specially if they are very long.

To find actual power consumption differences you need one of those power monitoring apps. (many options on the web).

Is it worth knowing? probably not, since you have to monitor it for like 2 hours, without other applications running to get meaningful numbers.