DAC Measurements vs Actual Experience


I have spent the last two days evaluating which of these two DACs I will be keeping:
1) Benchmark DAC3
2) PS Audio DirectStream

I'm foregoing the use of a dedicated preamp; the chosen DAC will serve that purpose.* 

I had read up on the technical side of each of these exhaustively before purchase. For those of you who aren't familiar, the Benchmark DAC3 measures quite well in every category. The PS Audio DirectStream, on the other hand, not so much. In fact, Audio Science Review places these two near opposite ends of its SINAD (signal-to-noise-and-distortion) list with the PS Audio being positioned near the bottom. Stereophile also provided measurements in their review that painted the PS Audio in an unfavorable light. 

And yet the DirectStream is proving to provide a sound that is more, dare I say, musical. It's a bit more relaxed, sounding a tad reserved in comparison to the DAC3, and the presentation of 100 Hz and lower seems to be slightly vague, but it's also less edgy, possessing a better soundstage, and is overall ever-so-slightly more enjoyable. So what am I doing wrong?

* Is it worth considering putting a dedicated preamp downstream of the DAC3 in hopes of gaining a more favorable sound? 
sixfour3
The psaudio has received many great reviews from pro to regular customers regardless of the measurements.
 I have one and love it even though I know there's dacs that measure better.
I've never heard a Ess based dac that sounded as natural and musical. 
When I can upgrade it will probably be for a chord, dcs or msb and not a standard chip dac. 

The directstream does also sound better with a preamp. 
The suite of measurements ASR runs through is meaningless in terms of making any purchase decision - granted it is one data point. Benchmark and ADSM both measure well, but ADSM sounds amazing and analogue but Benchmark sounds like POS.
So by that logic I can assume the ADSM sounds like a POS. Different strokes for different folks.
Analogue ... What exactly does that mean? Pretty much you are right YYZ
I guess the ADSM is the Linn ? I looked on the ASR site and see the Linn and Benchmark are very close on their chart. I've heard the Benchmark but not the Linn and at the price I doubt I ever will. My guess is in a blind test I doubt I could tell one from the other. Once DACs have reached a level where their performance is beyond human audibly I don't understand how they could be told apart. I have listened to other DACs in the same measurement range as these two and I couldn't. I know I'm deaf and my system is garbage.