I agree with a lot of this.
I bet the ODAC and E10 would sound MUCH more different with a different headphone (not sure if you tried lots of others). If you used both with say an HD-598 (or a closed headphone), then you would probably find that the E10 is darker and has more forward lower mids. I hated it with my HD-598 and DJ100. Sounded fine with the Q701 when used as a DAC. The E10 seems best with like a Q701 or a brighter headphone, but for me not so much with a much warmer (or bassier) headphone. I also didn't like it much with the PX100-II, which to my ears has lower mids that are too forward sounding with some tracks. The E10 I had made my 598 have painfully fatiguing and shouty mids, which makes no sense. Supposed to be ruler flat or something..
I don't know if you'll agree with this, but the HRT MSII seems a bit more revealing of my tracks. Why? I have no idea. They sound considerably "worse" with the HRT for whatever reason. Maybe it's because the HRT is more forward sounding in it's mids. I think perhaps the HRT might have slightly forward upper mids, but not sure. I think the HRT MSII is perhaps close to being dark, but not like the E10. The E10 doesn't seem too dark until it's used with an HD-600 or my DJ100. The only time the MSII seems kind of dark is when I used it with my HD-600 and K601. Hated it with those!! I blamed my amp for such a long time when all along it was 100% the DAC. Oops. Most would like the HRT MSII with the HD-600, but not me.
The ODAC seems a bit more smoother than the HRT to my ears. Some may prefer the HRT. Not sure why, but the treble from the ODAC reminds me of my "audiophile" PS1 (SCHP-1001). I probably couldn't ever get it's treble to bother my ears and this is on several amps and with the Q701! It almost seems too easy on the ears, but that's a positive. Even my garbage tracks that are normally very fatiguing are quite listenable with the Q701 and ODAC.
I always felt my Headroom Micro Amp had a small soundstage, but when I installed the ODAC it was quite a lot larger. Maybe the HRT MSII isn't a perfect match with the Micro Amp. I just know that the Micro is super duper revealing of what's connected to it. If I attached a Clip+ it sounds like a Clip+..well on steroids, but with the same signature mostly.
I do find it amusing how people say the ODAC will make the Q701 magically more analytical or revealing. Based on my experience this is definitely NOT the case. More like the opposite. I find the ODAC makes my Q701 sound even more musical
Sounds basically how it should and it doesn't suddenly sound thin or less full sounding. Still quite warm sounding, but obviously not like an HD-600.