Well, the main difference in tonality is that the HE4 is a little v-shaped. Kinda how the DT880 is known as well balanced, but slightly vshaped. The Alpha definitely has a leg up on neutrality. But that comparison is quite valid. The HE4 and AD would be PERFECT companions. Two of my very fave headphones, for sure. I'm still in awe at how open the AD sounds, despite it being closed.
The Alpha Dog bumps up a few notchs, HE-4 as well, with some cable upgrades. I have DIYed cables the last year, and if you believe cables make a difference, read what Peter Bradstock says about the Alpha Dog cable on his Facebook page. The stock Alpha Dog cable is really holding it back...cable upgrade makes if sound very close the the LCD3 (Peter's word's). I would be glad to add the HE-560 to this duo, hoping the single sided magnets do that for me, because they sure look comfortable!