I own both the VA Beethoven's and the N803's in two seperate systems. Here are my thoughts:
The 803's have a bigger, fuller mid-range than the VA's. It is also a more transparent and accurate speaker than the VA's. It excels in the mid-bass not the low bass. The nautilus tweeter design makes for both a tall and wide soundstage and pushes the sound way into the room. The 803's play much louder than the VA's.
Also important to remember that the 803's are like a well-muscled, atheletic but lazy football player. They have great potential but they need to be kicked in the ass (in terms of juice) to really hear them at their best. I'm not sure your integrated amp can really push them. They don't have particularly fast drivers nor are they the most dynamic speaker either. Proper electronics and cabling though can more than compensate for these shortcommings. They need a minimum of 200W from a high current amp and 300 is even better. 400W will make the them levitate in mid-air and sing for you! Power has a huge impact on these speakers.
The VA is a tighter speaker. Mid-range and bass are very tight with no bloat in the mid-bass. Overall, they image better and it seems you can pick out invidual instruments and players on the soundstage better than the B-dubs. The bass goes lower. This is a warm, romantic speaker that can be downright seductive with the right matching components. The warmth comes from both the mid-range and the tweeter. The tweeter is a silk soft dome and the pesentation of the highs is very different from the B-dubs. Not quite as detailed as the B-dubs but still plenty of detail. They have two different perspectives with the B&W more forward (first or 2nd row seat) with a wider soundsatage and the VA's more laid-back (mid-hall seat) with a deeper sound stage.
The VA's performance also improve's with more power but they don't NEED HIGH POWER to perform well like the B&W's do. Its a more efficient speaker.
To sum it all up, the VA's have a more focused soundstage, deeper bass, better imaging and are warmer and more romantic. I think the Shandling would add more of the same (especailly if you use the tube output stage) and make the music too syrupy and smooth.
The B&W's have a fuller sound, more mid-bass energy (which I prefer considering most music rarely goes below 40 cycles)a wider soundstage, are more accurate and are more transparent to the source components. I also love the fact that off-axis response of the B&W's is excellent (no matter where i sit in the room its a great seat) as opposed to the VA's which have a smaller sweet spot.
Belive it or not, for HT I prefer the VA's as that tight sound makes for a great thrill ride on well recorded movie tracks. Regarding music, I prefer the B&W's (sometimes) basically because of the fuller sound, wider soundstage, added transparency and slight increase in detail. But there are have been many times where on certain songs I have preferred the VA's. That lushness and sweetness is intoxicating and the mid-range can be down right magical at times. The VA's are naturally magical..whereas the B-dubs CAN BE magical when paired with the right electronics. Choice of speaker cables are also critcal for the B-dubs.
I have no experience with the AP's. Hope my comments are helpful!