What I primarily listen for(and you need software that has it recorded) is dynamic linearity(my handle). This is NOT dynamic range, the ability to play loud cleanly although that's a part of it. It's linear changes in level whether small.\, medium, or large, the lack or at least minimum compression. This is waht makes real sound real. It's not frequency response. Change your seat in a music hall and frequency response changes. And it's not distortion(as long as it isn't huge but thousandths of a per cent is irrelevant. Harmonic distortion is musical(hate that term). But clean, wide band sound without dynamic linearity sounds like a great radio but not like live sound.
P.S. This was explained to me 5 decades ago by Bud Fried(the name sake of IMF speakers) but it took me a few decades to understand what he meant.