I have heard both, but am not going to comment on the B&W 803 due to their terrible sounding set-up (small room w/ Krell monoblocks). I have heard other lesser expensive B&W's setup more correctly that sounded superior. I have heard the 802 model elsewhere, and I think they are something else, very musical, awesome speakers. But, imo, they look funny, just me.
Re the 1037, I am the type that tends to prefer more defined bass, even at the expense of it possibly being leaner. I think the one thing you will notice and pay attention to is the characteristics of the berrylium tweeter. In a way, I guess I might agree that it could be possibly be called sweet. It is incredibly, incredibly detailed. However, the presentation, imo, is quite forward (though not as bad as with the 900/Profiles). Also, any old recording (I listen to mostly classical) will be given a very, very unforgiving rendition possibly loaded with sibilance. It IS the cd's fault, but I still want as many of my cd's to sound good. If your collection of recordings was done more by the sq than musical performance, you may have found your match.
This is simply the opinion of a newborn audiophile/consumer. These dealers work with them everyday, so they will know better, and will have opinions on components that maximize the synergy. Still wanted to throw my two cents in.