I do agree with your observations about the quality difference having shopped at both PS and Press. However, beyond the quality is a different style as well.Flanderian, I think you're correct in your observation that there is little overlap in PS and Press customers, but you're not attributing the right cause to that phenomenon.
The reason there is no overlap is because the people who buy PS want quality, quality which Press doesn't offer. However, many PS customers grew up on Press, attended campuses on which a Press is situated, and likely wish that PS offered clothes closer to what Press offers, just better quality. Paul Stuart offers many nice things, some of which are just plain weird, others nearly unwearable unless you're in a retirement community in Florida.
Remember that most men aren't too active in their clothing selections. They go to BB because that's where everyone else who dresses properly and has a respectable job goes. When they get a bit older, perhaps earn higher salaries, and if they live in NYC, they go to Paul Stuart, because that's what a man of a certain circle does. So, in a way, Paul Stuart is chosen for many of its customers, not the other way around. If Paul Stuart offered more traditional American clothing, these men would still shop there. Similarly, if Press offered clothes of better quality, then PRESS would be the place people just go, and Paul Stuart might not be.
My point is that Press misses out on an opportunity in the US market.
Press still offers the TNSIL look although my understanding is that the have strayed from the NS for a time and come back to it. PS offers more of Anglo look with the suppressed waist and double vents. My PS suits both have great natural shoulders. Maybe if PS moved to more of a TNSIL look many of its customers would be oblivious. I don't know.