Not sure if it's related to where the audio is sourced from (MP3 vs CD, etc) but I've always really noticed that there is a huge disparity in quality of audio processing of some stations.  Stereo separation, overall volume, modulation, lack of distortion or being overly "bright", noise floor, 60Hz hum during quiet passages in music or lack thereof, etc. 

Some of the best major-market stations I think I've ever heard in that regard were Tulsa, Oklahoma.  Perfect audio processing.  Wasn't even in Tulsa, was actually Wyandotte, but that's beside the point.  Stereo separation was particularly good as I recall. 

One of the best translator type relays I've ever heard audio processing wise was K21T6AA, a relay of KFSK, Petersburg, AK.  I'm on the fringe of it here, where it barely pops into stereo at all, but within its 60dbu type contour or otherwise in its 'local' listening area, it was also amazing in terms of stereo separation, perfect volume, and the like...maybe a little over modulated but not bad.

I've also heard far too many translators through phone lines and in mono...those are awful.  Also many stations sometimes try and cram as much volume in as they can, or overly compress their music. 

A particular pet peeve of mine is "pitched" audio, or the speed of music up a couple percent.  I can't stand it personally.  A couple major-cluster, albeit iHeart-owned (go figure) stations in Fairbanks, AK at least used to do that.  I hated it. 

Ironically, one of the aforementioned Tulsa stations was an iHeart-owned one.  I've actually heard a couple active-rock iHeart owned stations (KMOD in Tulsa and KZPR in Minot, ND) that rocked surprisingly hard, especially for iHeart standards.

Here they have 'HD Radio' which is a digital broadcast, but it works off the existing FM or AM transmission (no need to stop broadcasting analog)

It is not really true. Because it occupies the space FM receivers are designed to work, so by that prevent more analog stations being there.
I think using separate band for a different, incompatible, modulation (at the end it is just another form of modulation - a different way how to carry sound over radio waves) is way better idea than occupying the band some other was designed for. Because the new modulation requires new equipment anyway, the fact it uses diofferent band is no further burden at all.

And if you look carefully into the ITU bandplans, the band now used for DAB was allocated for HiFi broadcast since the late 40's (although the expectation back then when it was allocated was to use wider FM there). But till DAB any broadcast there never took off commercially. First the 3m FM capability was better than the mass produced radios allowed till the 80's anyway, and second the shorter wavelengths means worse signal spread (shadows and reflections) along environment obstacles, so it would require external antenna like TV does. But that is something only acceptable with really large, high end receiver installations, not with the common radios.
The difference is, unlike DAB, the FM does not allows the signal to be distributed by multiple transmitters working in the same area on the same frequency, so was stuck only where the single transmitter may reach And if there was a shadow behind some building or so, or strong reflections, the reception becomes impossible.
It is because the DAB allows that synced transmitters (and the reflections improving, instead harming the transmission), it became possible to go around the obstacles by using multiple smaller transmitters, so it became practical for consumer use (so suffice with just a whip antenna on the radio itself)

I personally don't mind AM and would listen to is as I find it to be more reliable with the smaller frequencies and the fact that it can travel further at night. I generally listen of FM though as that is where the music stations are, my favorite ones are 104,3MHz, 80, 90s and 105,1, the local rock station but just recently an AM station got taken over and now a new music station, 1278Khz and there seems to be a pirate station at 1629Khz.