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? 
Contrary to what this implies these two concepts are not mutually exclusive. 

You do you and carry on with measurement first mentality. I use my ears and keep the equipment that sounds good to me.
@rbstehno I don’t understand what you are trying to imply here. I write about stuff I own and heard. I do have a lot of experience with Linn DS as I have owned various DS over a decade. I don’t talk much about my Ayre and Chord front end because they don’t sound as good as top of the line Linn DS. 
Re the Klimax in 2011, it was a true revelation back then. Playing 320k mp3 from Linn Radio was a treat. 

@djones51 To me “measurement first” subscribers will keep a piece of gear solely because of measurement even if this gear is steering the person to listen to certain kind of music. “Listening first” will get rid of a piece if it sounds bad to that person even though the gear measures well. 
I believe “measurement first” and “listening first” are mutually exclusive. 
You give two different parameters. I look at measurements first if it sounds bad I don't buy it or keep it. The type of music I listen to has nothing to do with the components I buy. A DAC doesn't steer me to listen to certain kinds of music. 
Looks like we are all in agreement here. I approach buying gear in pretty much the same way. I eliminate truly horrendous measuring gear (like border patrol) and then see what’s available near me for audition.