Though I'm no expert, I did play sax for a while and have been around them even longer. I would expect that the reason for getting the best sound in the above manner is because, while most sound does come from the bell, sound also comes from the body.
I would try both mics at first. Not being a mic expert I might expect you'd get a bit of a better sound from the AKG. But, if you like the sound of the 57 go for it and use the C3000B as either a room mic, or (a bit more interesting in my mind) would but to put it near the neck to capture the natural sound of the breath, the keys, and what not. (I've never done that so I'm just going on theory.) It all depends on the sound you want. Using it as a room mic would probably give you a more "polished" product, where putting at the neck might give it a more "intimate" feel. Just some thoughts.