Or, is the reason for going moving up the Axiom line (or other subwoofer manufacters, as well) just a matter of extension and high SPL capabilities, needed as rooms get larger.
Yup. That's exactly it. You will benefit from lower extension in a small room as well. In movies, there is significant content below 20 Hz (kaboom!
Think about it this way. If you take a ball of string and cut three sections to exactly 3" using a razor blade, scissors and a cleaver. If you mix them up and lay them side by side, can you tell which was cut by wach instrument? No. That is because the instrument used does not change the nature of what you have created.