Ipad pro + Ethymotic Er4 SR, brilliant

I am not sure of the exact configuration you used, but the DAC/Amp is, IMO, in the dongle that connects to the IPAD.  I recall it was tested on a respected web site and it measured very well.  

I am not using a dongle but just an adapter, no dac in there

Yeah, the iPad sounds good until you compare it to something better.  I added an Audioquest Dragonfly Red and ditched the Apple Camera Adapter for this…

https://www.lavricables.com/cables/reference-silver-lightning-interconnect-cable-for-oppo-ha-2-centrance-mini-m8/

I too thought the ipad on its own sounded pretty darn good and is super simple and convenient, but once you do some upgrades as above you realize how limited and compromised it really is, especially if you have good headphones/earphones, which you obviously do.  Just my experience FWIW.

@soix 

you must be using an older ipad. The ipad pro has usb-c rather than lightning adapters and your part doesn‘t fit.

I still highly doubt the DAC/amp in the iPad is superior to something like the Dragonfly Red or Cobalt, but as long as you’re enjoying it that’s all that matters.