Not really only Doppler shift - the loud thumping 'wok wok' noise certainly sounds louder when it's coming at you, then as it passes overhead and heads away the tail rotor noise becomes more apparent and the 'wok' drops away relatively quickly compared to when it's approaching. It doesn't seem to be simply a pitch shift thing which would be explained by Doppler - I reckon it must also propagate more in the forward direction of flight. There's a doctoral thesis for someone - investigate Huey noise!
The Chinook makes a bloody loud thump too, but there's not the tail rotor buzz superimposed, so you can tell the difference before you see them.