I have had both. They are very similarly voiced (obviously, as they're children of the same father). The midrange on both is very, very similar; usually I could not distinguish them. At first, the NAD seemed to have a slightly more transparent top end, which Tyll reported. But the bottom end of the NAD wasn't quite as extended as that of the PSB, which made me think the NAD sounded thinner. I found that the PSB were more comfortable, perhaps because the shape, size, and angle of the ear pads bothered me less than the NAD's. And because of the way they fit, the PSB gave me a more extended bass range and the overall presentation seemed more cohesive and enjoyable.
Over time, I found the fit of the headphones to affect the sound more than I had thought initially. Measurements are just one factor. Unless you can measure a set of headphones ON YOUR HEAD and relate that to what you're hearing with different models that you wear or are measured on something that replicates your own head, take all measurements with a grain of salt. Kind of like "your mileage may vary." I just could not get comfortable with the NAD; on my head, they fit more loosely than the PSB (but neither is a vise!) and that definitely affected the bottom end of their range. Some slight added pressure on the earpieces, just a bit of pushing with my hands, would change the perceived response and heighten the bass, but I would not be able to tolerate that kind of pressure if it came from the headphones alone. Neither of these headphones is designed to let the user modify the pressure and fit in any significant way without risking damage, which is too bad. They're definitely not adjustable for pressure and angle like some other headphones, and the NAD is very limited because of the square shape of the headband and the one-way spring loading on the earpieces.
It wasn't until I got my Oppo PM-1 that I was able to make a clear decision between the NAD and PSB as my set of closed cans. The Oppo is one of those headphones that people report as letting them listen to music for extended periods of time - as compared to listening to headphones. This happened more when I was wearing the PSB than the NAD. And the Oppo's gorgeous bottom end made me realize even more than before that I need to have a significant but clear bass response in any set of headphones, perhaps because that's what I expect when listing to speakers (I guess that's what Paul Barton terms "room feel"). So in sum, the balance and overall presentation of the Oppo just draws me in (and their bass response, like many planers, is phenomenal), that focus on the music happened more when I was wearing the PSB than when I was wearing the NAD. So I sold the NAD.
Neither of these is going to win any prizes as to the way they look when you're wearing them; I think most people would look at you as wearing something odd if you were out of doors, because of their shape and/or size. But as far as closed headphones go, you really can't go wrong with either one. Pick the one that fits you the best. Yes, the NAD is more portable than the PSB. But I have the V-MODA XS if I want to wear something away from my desk or a comfortable chair at home.
Paul Barton's future headphone designs will be well worth listening to, especially if he can get a more ergonomic and visually pleasing context in which to deliver the same kind of sound.