Good measuring DACs vs.

Measurements are grossly inadequate as they can only approximate dynamic conditions.

Most commercial Dacs measure well, but they sound grossly different. 

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.

I have tried a dozen or so DACs at wide price levels, wide technology differences, bad measurements, good measurements, no measurements. I don't know why this is but I have had highly rated DACs sound not as good to my ears as ones costing 1/4 price no one cares to even write about.  But while some may not sound as good in one system when I swapped it to another system in the house, with same source but different amp and speakers, and it sounded great. That led me to trying different ones in different systems (I have 4). I finally thought I had it figured out and so bought a higher/better/pricier model of one of the DACsfrom same company for one system and it sounded worse than their cheaper less capable model. Room/amp/speaker dependent? These DACs have included ones with various filterings, two chips, one chip, different chips in otherwise same model, R2R, NOS, and so on. I finally stopped when I thought stuff sounded good. It is like balancing a fulcrum. When you get it slowly back away and don't touch anything.

I think that one premise that a lot of people seem to accept is that distortion always sounds bad. Any change from the input signal is distortion. So all the things that studios do to make recorded instruments sound “better” are distorting the signal. Noise is another thing, but I don’t think the human ear is that sensitive to noise if it is constant. Listen to Take Five on vinyl. Loaded with tape hiss, but still enjoyable.

DAC measurements are the least reliable of all, especially since they tend to concentrate in the D rather than the A side of the DAC. As per Erik Squires, most modern DAC chips measure excellently in terms of their linearity, so most of the current measurements don't give any idea of sound quality of the finished product.