If you take a deeper look, things can look a bit more complicated and different. Here is a comparison using woofer driver datasheet information from SB Acoustics.
The 8 in. one has an effective piston area of 216 cm^2 and a linear coil travel of 1.3 cm. Three of them will give a displaceement of 3 * 216 * 1.3 = 842.2 cm^3.
SB23NBACS45-8 8" Black Aluminum Cone Woofer-234mm- 8 ohm
www.madisoundspeakerstore.com
View attachment 299851
The 12 in. one has an effective piston area of 508 cm^2 and a linear coil travel of 2.0 cm. One unit will give a displacement of 508 * 2.0 = 1016 cm^3, which is 20% more than three 8 in. ones. (Max excursion of a speaker driver is usually proportional to its diameter too.)
SB Acoustics SB34NRXL75-8 Large Magnet "Norex" Natural Paper Cone Woofer- 346mm- 8 ohm
www.madisoundspeakerstore.com
View attachment 299852
Moreover, we are less sensitive to distortions at lower frequencies, so the subwoofer can go at it harder only reproducing the low bass frequencies at higher distortions, without "contaminating" the upper bass. Below graph is from the ANSI/CTA-2010-B (Standard Method of Measurement for Subwoofers). Band 1 is for the 20-32 Hz octave, band 2 is for the 40-63 Hz octave, and band 3 is for the 80-160 Hz octave.
View attachment 299853
You can see that the acceptable HD+noise threshold gets progressively lower as frequency increases. If you have subwoofer(s) reproducing the low bass and the woofers in your main speakers reproducing the upper bass, the sub(s) can run a lot harder without negatively impacting the quality of the upper bass.
This Standard defines a method for measuring the audio performance of powered subwoofers, both passive and powered
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