You may want to read the "Comparison" in this.

I would encourage you to try both systems if you don't mind taking a chance on the return shipping for the Axioms. I'd be willing to bet that the Axioms will stay put though .

Regarding the subs, I'm of the opinion that the 500 will definitely be louder, go deeper, sound more transparent, blend better with your other speakers and be smoother than the Aperion 12" sub. But the Aperion may give you more "punch and snap" at the expense of all the other attributes I mentioned. I am making this assessment by looking at the frequency response graphs. I also wouldn't be surprised if the Aperion sounds "boomy" given the hump that develops right around 55Hz.

Whatever you choose, we would be most grateful if you let know how it sounds. Good luck.