I have all three (ER4S, ER4P, and the Stax SRM-001).......Hey, I'm not the "Keeper of the 'Phones" for nothing!
My impressions of the three are as follows:
In comparison to the Etys (both S and P versions), the Stax has bass that can be felt. It is not all that deep, but it is well-controlled, and provides just enough "thump" for my tastes. As has been posted numerous times, the Ety bass is heard, not felt.
The midrange is wonderfully transparent on both the Etys and the Stax, but I feel the nod goes to the Stax. Cymbals, acoustic guitars and horns are reproduced with uncanny realism.
The main drawback to the Stax is it's rolled off high end. I suspect this may be a fault of the amp that is supplied with it, but since the plug is a dedicated one, I have no way of testing this theory. In comparison, the Etys have a very extended high end......with the 4S being a bit smoother and more refined than the 4P, IMHO.
As for comfort, I prefer the Stax, once I adjusted the headband to provide very light pressure. They don't go into the ear canal, as the Etys do. Rather they rest at the entrance to the canal. However, there is virtually no isolation from external sounds. In this respect, the Etys are far superior, if isolation is important to you.
To sum up, the Stax are exciting headphones with a nice bass and fantastic midrange. Because of their rolled off top end, they can actually make older recordings (ie. Billie Holiday) sound wonderful. The Etys are more neutral sounding, with a more balanced presentation. Hope this helps.
I'm sure JMT can also offer his impressions if he so chooses.........but we don't want to take him away from his amp building now, do we?