I've tested both headphones very long with the most varied music, from classical music, piano music, through rock, jazz, pop to drum'n'bass. Both headphones deliver great sound, in principle, one can make a mistake with any of them. I was long undecided which one to pick, but then yet decided on the Beyerdynamic. It took some time to find out why I like the ATH in the end not so good. The sound is definitely loud and clear, in comparison to Beyerdynamic even louder (logical, since lower ohm-number) and powerful. But in the long run it has annoyed me. The sound is more direct at the ear, too intrusive in my opinion, anyway you will be tempted to hear louder than you actually want. Overall, the ATH then acts to overemphasized at me, at higher volumes also unclear.
The Beyerdynamic is neutral, yet clear and brilliant and spatial, it makes a bigger stage on. This was in polyphonic Baroque songs most clearly. However, it might be too quiet for some fortuitous on iPhone almost. At the plant the sound is again better, especially in the lower range.
Conclusion: The ATH is a nice headphones which provides a somewhat exaggerated sound, but I was too stressful in the long run. I have therefore decided to use the more neutral Beyerdynamic.