For what it's worth, it's very clear to me which is better even on my iPhone's speakers (as well as on my desktop's "real" speakers, of course). Sound preferences are deeply personal, but I'm still pretty shocked GP can't tell.
This is actually a common misconception. In blind testing, the average listener reliably prefers the more accurate speaker. There is a talk [1] by Dr. Floyd Toole that is an excellent crash course on the science of sound reproduction and listener preference.
I listened on a calibrated speaker setup and on my good Sennheiser headphones. Yes, there’s a difference, but both sound like shitty speakers just with different EQ profiles applied to it. It's still compressed to hell and extremely tinny no matter what.
I agreed with this so I made the levels equal (as measured objectively with EBU R 128): https://0x0.st/HvXA.wav
The first (DSP processed) clip still sounds much better to me. The first time the unprocessed clip is played it's rather noisy for some reason, that could be room noise picked up in the microphone though. The high end is missing from the second clip almost entirely (anything above 5 khz).
However the DSP clip isn't without significant problems. It sounds distorted to my ear, and slightly pitch shifted as well. It's rather "tinny" sounding. I'd rate both clips extremely annoying to listen to in comparison to the original which seems pretty well mastered if you like this sort of thing: https://youtu.be/ZRtdQ81jPUQ?t=52
It's hard to tell how much of this is due to it being a quick and dirty recording. Also, being able to play audio at higher volumes is supposed to be one of the big advantages of using this DSP chain, since temperature spikes created by transients are managed in software. (Just speaking for myself personally, I've never felt that my non-Apple laptop speakers needed to be louder, even without DSP.)
The big issue I see with trying to compare the DSP profiles of two different clips, as recorded by a cheap consumer microphone in a compressed audio clip is that we're unable to tell whether asahi's DSP is actually better or just happens to match the sweet spot of the phone's microphone DSP profile.
That's precisely the issue I've got – yes, there’s a difference, but both sound like shitty speakers just with different EQ profiles applied to it. It's still compressed to hell and extremely tinny no matter what.