The sub-bass extension of a driver is determined by its resonance frequency, not by its size. Assuming equal excursion capabilities between a larger and a smaller driver, the larger one should always produce a higher sound pressure level above a certain frequency. However, the point at which it begins to roll off is dependent on its resonance frequency, not its size. It is possible for a small driver to maintain a flat extension down to 14-15Hz, but distortion will become excessively high at anything above low listening levels.
The resonance frequency of a driver is influenced by its stiffness and weight. A driver that is very heavy and made from a soft material may have better extension capabilities.
Below you can see the free field response of B&C 21 IPAL, one of the loudest 21 drivers ever designed, if not the loudest:
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as you can see its response starts dropping below 100hz. Of course it is possible to tune it lower with different enclosure design methods.
Here's SB Acoustics 10'' driver, SW26DBAC76-8BLK 10":
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Rolls of very smoothly and slowly down to 15hz.
One is a 10'' driver, other one is 21''.
This is of course against human intuition. How can something larger can produce lower sound levels than something smaller in low frequencies? The reason is, the efficiency of moving a light-weight/stiff driver in low frequencies become so low that, the power required to make it push enough air becomes extremely high. Resonance frequency is where a driver can be moved most efficiently and outside of that frequency, the drivers tend to become less efficient.