The MDR-1000x (and all NC models, for that matter) are engineered to be best used in NC mode. The choice of materials, size/space, and other various aspects are all done a certain way to make them sound the best they can. Want evidence? Compare the MDR-1A to the MDR-1000x in passive mode. Same driver, different sound. This is specifically why Bose prevented you from using them powered off -- so people didn't judge them if used the wrong way.
They sound dramatically different in full passive mode, and yes -- there is a huge chance the built-in electronics will sound better than our DAPs and DAC/amp stacks. digital amplification with direct delivery custom to that of the makers of the headphone = winning. It's not that our separates are not fantastic, but not the right tool for the job (wireless audio) I wish there were more non-NC active headphones. I see V-Moda just did that, maybe more now that wireless is gonna be huge with the arrival of Android O (LDAC, AptX)
**edits for clarity**
True, I actually went with my 1000xs at the AVstore yesterday to do some tests after reading some reviews here on the website, critical of the 1000xs performance. Started doubting my initial decision a few months back. I used to have the MDR1A, and I ended up with the 1000x. I got the MDR 1A after testing against the ATH7, momentum 2.0, h6 and P7 to select a nice portable headphone, and had it paired up with a Fiio E17K, until I came in contact with the 1000X.
So i went to the shop to see if I can get smething on a similar budget as a 1000x. I'm talking good passive portable headphones with a portable flash sized DAC for optimum portability. Naturally I tested the excellent DragonFly RED. After going thrugh a few headphones I settled, unsurprisingly, with the 1A again.
The MDR 1000x with the DragonflyRed powered OFF, sounds really bad, cannot compare it with the 1A, even though they have the exact same drivers. But powered ON it sounded extremely similar. Tighter soundstage, but crisper low and high ends, but overall similar in tonality and warmth. However the bass on the 1000X would start clipping and distorting after going 60% volume on the Dragonfly (which is in anyway beyond enjoyable), but the 1As started distorting at 90% (the 1A are really good).
Overall the 1A + Dragonfly sounds better, obviously, but by a suprisingly slim margin. I expected much more air to the sound, but no, just a bit more finesse, volume and soundstage. Dynamicly the 1000x is just as flexible powered on plugged into my Xperia XZ than plugged in the Dragonfly, or the 1A plugged in the Dragonfly for that matter.
Theres a much bigger difference in 1A + Xpeira XZ vs 1A + Dragonfly, than 1000x + XZ vx 1000X +Dragonfly, as in the 1000x sounds significantly better powered on in my XZ than the 1A, but when connected to the Dragonfly, it doesn't sound that much better, or vs the 1A plugged in the Dragonfly (except of Volume, i'm only talking about quality : dyamics, soundstage, smoothness).
That proved to me one thing: a) I'd rather have the 1000x with their extra features (near high res wireless, touch controls, ANC) than a 1A (or equivalent) headphone with the excellent Dragonfly RED for roughly the same money (at the shop I went to, the 1000x was 20$ Short than the 1A + Dragonfly RED). Of course, If you get a more expensive headphone, like the Oppo PM3 which I tested and are 100$ more expensive than the 1000x, than it would sound much better with the Dragonfly red. But even the Oppo PM3 are not as advantageous, ignoring the ANC, buecause plugged directly in my XZ, for an optimal portable experience, they sounded way more anemic than the Powered on 1000Xs.
I must mention that I always use the DSEE HX option (under 24-bit music upscaling) ON on my Xperia XZ.
And all this has to do with the way the XZ are tuned in harmony with the in built AMP (S-Master HX high res digital) and DAC. They are so well calibrated, and this must be valid to some other top ANC current era headphones. And that's why a 1000x with ANC on, and very likely something like the Sennheiser 550PX, etc, sound suprisingly good when plugged in.
Remember, 99% of the reviews talking about 1000x's, Q35s and 550PX's quality are judging it from a wireless point of view. I've seen remarkably few 1000x reviews that talk about the sound experienced when plugged in. And cosnidering Sony sells the 1000x with a 1,5 m OFC high quality 70$ cable, it's a bit surprising. Because that's when they shine and walk into premium wired headphone territory, not Wireless. It also ads to the versatility of high end wireless ANC headphones in this category.