Energy loss in the doppler effect?

[p.tryon]

If the energy of an EM wave = h x f
and when a light emitting body (of a particular power) is moving toward or away from the observer the observed frequency changes, does the energy change?
If so where does the gained or lost energy come from?

 

[Hootenanny]

Energy, is of course, reference frame dependent. Consider the classical scenario of two cars traveling towards each other along a road, you are sat in one car. Each car is traveling at 30mph relative to an observer who is stood stationary on the road.

Now, if you (sat in your car) 'measure' the kinetic energy of the other car is it going to be the same as if the stationary observer 'measures' the kinetic energy of the other car?