IMO axioms subwoofer design is more setup for home theater type bass than music. I'm no expert, but the magnet on the back is comparably small when set next to a high end car audio style subwoofer. I assume the large magnet (and high power amp) allows deeper, tighter and faster bass. Which (along with something else) I enjoy as often as possible.
Like you said you're no expert and neither am I, but basing your conclusion on what you see is very amateur, there is much more to a sub than the total size of the driver, magnet and watts available, the way all of it interacts is the key. Axiom's driver has a very low resistance thus they can get away with smaller amps and magnets. It just takes less power to move them.