The DAC in the H390 is good. I had a 390 briefly and have a 590 I use frequently. I have had issues with Airplay and it constantly dropping. I assume you aren't using Airplay. How are you getting a signal to it currently?
There are much better external DACs that will deliver better staging and will be more detailed. They are not inexpensive though. I would put the on-board DAC in the same league as the Chord Qutest or Questyle CMA 12. Good DACs but you can do better in terms of staging and/or detail.
A big part is budget and then what do you think might be missing with what you are hearing now?