I’ve tested a few pairs of earphones and a pair of headphones (Very noisy: Sennheiser IE80, no noise: Philips Fidelio X2HR, Phonak Audeo PFE 112) and it looks like ones with 16 Ohms impedance exhibit a lot of noise, while 30 Ohms and up ones are silent.
I’m not sure if both have a separate audio board. I’ll try with my Senfer DT6 as well, those are great and relatively cheap. I also have some other in-ears and headphones, to confirm that the impedance is the important factor.