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? 
@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. 
You have come to the point of recognizing that what measures well doesn't ensure sounding well. Conversely sounding well doesn't necessarily correlate with measuring well. IMHO listeners are in the long run much better off choosing audio components that sound best to 'their own ears. It doesn't matter what others may think or hear differently than you. It's purely subjective.  Just be happy and select what you determine to be the better sounding more satisfying component. 

As this thread has clearly demonstrated people are simply going to disagree on how a particular audio component sounds. Some posters here find Benchmark to sound excellent and others aren't impressed with them by any measure. In my own encounters with this brand's products they struck me as clinical/analytical/sterile. If you find the P.S,Audio DAC more enjoyable and engaging,  trust your own ears. I wouldn't obsess over the measurements at all.

Many issued recordings are flawed in some way or other.  Perhaps most are.  If you are a certain kind of purist who wants to hear exactly what the recording as issued is presenting, then by all means get the most "accurate" components possible, which is something a lot easier to measure with DACs than, say, loudspeakers.  If you want to sit entranced by most if not all of your collection, you may prefer something else.

For instance, I remember the early Deutsche Grammophon recordings that were recorded digitally and issued DDD on CD were usually pretty much unlistenable.  Things have improved since then, but still...

Is orange a "distortion" of yellow?  If you happen to like the color orange over the color yellow, is that wrong?