Haha, I wouldn't even attempt to answer that question without a proper A/B switching setup.
I recently was comparing a powerful but quirky Chinese amp, and I swore it sounded vastly different comparing the SE of it to the SE of my Project Polaris, but it turns out it was a case of not (1) volume matching closely enough and (2) the ephemeral nature of audio memory, because I once I compared using an A/B switcher, with each of the amps' headphone outputs going into the switcher and my headphones plugged into the single output of the switcher, and a toggle that could instantly go back and forth between them, it was easier to volume match and then compare the differences in sound.
It turns out there was very little difference in the sound -- there
were differences but not nearly as drastic as I had imagined before.
But testing the balanced out and SE out of an amp would be a lot more challenging and would require a better XLR-capable switcher (I have my eyes on one on Amazon) that accepts two sets of balanced inputs and an RCA input and can output balanced or SE, and then ideally, two LCX's (which ironically I did have for a short time but no longer have) so that you could instantly compare the SE and balanced out with one pair of headphones -- toggling between one LCX outputting balanced out and one LCX outputting SE.
Otherwise, I would be very suspicious of anyone making claims about sound differences between SE and balanced of an amp except for the obvious power output, which we know on many balanced amps are different between balanced and SE due to the internal design, and which even audio memory as weak as it is can even detect readily out of the LCX, it's noticeably louder out of balanced with the same pair of headphones at the same volume setting on the LCX vs when I use a 4-pin XLR to SE adapter and plug them immediately into the SE output at that same volume.
But I suspect other differences people hear are often (not always, I'll admit) attributable, in truth, to the ephemeral nature of audio memory and differences in power output, mixed in with expectation bias. I wonder how many people would be able to tell the difference in a double blind setup?