If you connected your Bose speakers directly to your reciever I would expect them to sound worse. The Accoustiumass box is not really a sub , it is designed specifically for the Bose cubes. I'm a former Bose owner and I would agree there is no comparison between Bose and Axiom or a similar great sounding speaker.

A computer once beat me at chess, but it was no match for me at kick boxing.