First and foremost, I need to emphasize that my listening room is FAR from optimal. 11 m2 on the 2nd floor if a wooden house, there is a major bump around 65Hz and a loss of energy between 80-100Hz, some up'n'downs after that. The sound is quite thin, but with bigger speakers the 65Hz bump becomes a showstopper (having owned bigger Proacs and PMCs, with whixh also the treble was too much). 10 cm behind the listener's head is a window. Thus, don't take my word on which speaker is better. But better behaving in this room and positioning - A1 over P3ESR, yes. Slightly more forgiving, a little less detailed, more even bass, easier treble. I can hear the virtues of P3ESR, but still want speakers that work better in that room.
The Accuphases are most likely an overkill as their talent is lost in my room (should really try another amp to be sure!) In any case the A1s can disappear totally, they image with pinpoint accuracy, although some 3D is lost for me as I keep the speakers so close to the wall to help low-volume listening. Esp. male vocals are presented well. Bass in A1s becomes a bit soft-edged when very fast drumming is required. This may be due to the Custom Design stands, though. In the lower treble there is a shine (sorry for no better word) of which a part of me likes.
I opted to try a Dspeaker-corrected sub to fill the hole at 80-100 Hz. It seems to eat some accuracy but the room seems to need it.
I am not in final, however. I'd like to try a bit more kick and groove, but then, fatique may become an issue. My previous speakers were PMC Twenty5.22s with the aforementioned virtues, but A1s on me over with the balance.