As far as I know, below a certain level of distortion and frequency response flatness, there’s very little correlation between better measurements and better listener preferences.
Just like with amps. Below around 0.1% distortion, the specs that we commonly use rarely help us know what will sound "better."
In other words, almost all DAC’s have very good measurements, especially compared to what was out in the 1990’s. What sounds best to listeners has never been proven to correlate, though there are successful designers like Nelson Pass who argue strongly for certain types of distortion being better than no distortion, and his commercial success speaks for itself.
Personally I seem drawn to DACs with AKM chips... but I certainly can't say it's true always. I used to really like Burr Brown based DACs as well. Ages ago. No measurement to point to and explain it.