Obviously not, since you can get the same "better" sound quality by turning the volume up further.Also saying that the lightning port is louder and will be perceived as "better", then wouldn't that still be a reason to say that lightning is better?
BTW, it would have been more interesting to hear how the volume of these headphones compares to, say, the Apple earbuds when using the 3.5mm jack. If the headphones have lower sensitivity, they take more power to drive, which means that the main difference of the Lightning cable vs. the 3.5mm jack is probably that the amp in the cable has a higher power output (and draws more power from the phone's battery accordingly).