I have now listened to Superwoman and No One from Tidal Hifi via my Chord Mojo (connected to my MacBook Pro, exclusive mode in Tidal) connected wired to my P7W and my PX (ANC off). I am no expert in describing the sound, but these are my thoughts:
No One: the bass thump is clearly more present on the P7W than on the PX. The overall presentation is smooth, the vocals are nice, but maybe a bit thin (compared to the bass thump). On the PX, it sounds slightly more boxy, the bass is weaker, but more tight (I think). The sound stage is bigger on the PX and the vocals sound a bit fuller. When switching between them the P7W sounds like they are missing something in the mids (I think). Overall, the P7W sound nice immediately when putting them on, but the PX sound like it is more balanced.
Superwoman: On the PX the instruments in the beginning with the organ (?) are very well separated and the vocals come in nicely. On the P7W, the instruments in the beginning are harder to separate. The vocals are nice, but feel a bit thinner. At 1:12 when more instruments and bass come in, the PX separates them better, but the bass is stronger on the P7W.
I don't know exactly how to describe this, but my main impression is that when switching between them the P7W sound more bass heavy and smooth, but missing some parts (in the mids?). Again, when switching back and forth, the PX sound more boxy, but with better instrument separation and wider sound stage and more balanced. Vocals sound a bit fuller. I also get the feeling that the slightly boxyness to the sound of the PX goes away when you listen to them for longer periods and get used to their sound, it is only when switching back and forth you notice it as much. The P7W are more inviting in a sense, but PX more revealing. The P7W sound good immediately, but the PX benefits when you give them more time. It is hard to say that one is better than the other, they are different.
Just for fun, I also compared with my Focal Elear connected to the Mojo in the same way and it is (as expected) clearly better than both. Compared to the PX the Elear have a stronger bass, even fuller vocals and a bigger soundstage without any hint of boxyness. This is of course a completely different beast of headphone being open-backed and in a different price range.
After having used the P7W for quite some time and the PX for a few weeks now I have really started to appreciate the sound of the PX as it sounds more balanced and with better instrument separation. Bass is weaker, but tight. When I put on the P7W they sound inviting, but with an exaggerated bass. I do have one problem with the PX though and that is listening fatigue. I get much more tired listening to the PX than the P7W. I don't know if it has to do with the angled drivers shooting sound directly into my ears, the dynamic drivers or the tonality. It does bother me though.
there are only two things that cause me listening fatigue, over-emphasized bass and bright signature. with the PX, it is more likely the bright signature since I found the bass not that fatiguing. I have to lower the volume down to 30% each time as I found the brightness too much like listening to a brand new set of speakers before burn-in. some people suggested to burn-in the PX for a while with pink noise. from the looks of it, it might take awhile for the PX to reach their optimal performance if 2 weeks isn't enough. maybe 24-42 HRS of continuous playtime might do the trick.