At the risk of rocking the boat, how much does it really matter?
I recently bought a DAP, its not an overly expensive one but it is rather nice, a Shanling M3s. I cannot honestly discern a difference between the SQ at the same volume compared to my Sony XZ Premium smart phone, however what it can do is go a lot louder than my smartphone and even if I do not want to blow my ears up it can go louder before hitting distortion which is good. So really the benefit is not with the DAC, but the higher headphone output.
If using it outside background noise (regardless of headphone sound isolation or noise cancelling) will be far more deleterious to the listening experience than any differences in the DAC.
DACs do measure differently, that is a demonstrable fact. However in terms of audible differences I think DACs achieved transparency years ago and any audible differences there still are are pretty insignificant compared with differences between headphones and speakers. However, what does make a big difference is headphone output given the anaemic output restrictions on devices to comply with hearing protection levels.