If we move towards a source of EM waves, in our reference frame the frequency appears (and it is) higher than what a stationary observer will see due to Doppler effect. The field transformations show that these two observers will se static fields differently so I would also expect that the peak amplitudes will rise in the moving reference frame. Also the wave momentum should increase and total energy of an EM pulse. This is what happens when we analyse objects. If instead of a source there is something that launches an object, in the stationary reference frame the object will have a certain momentum and energy, and in the moving reference frame the energy and momentum will be higher, with both frames being equivalent and valid.