The LAB12 woofer is a good driver, but its motor is a fairly common ferrite structure without a shorting ring. In the three π cabinet, excursion is lowest when the sub is used above 20Hz. Below that frequency, excursion and distortion rise rapidly.

The 12π basshorn subwoofer has three mechanisms that reduce distortion. One is push-pull drive, which works at all frequencies in the passband, but only reduces even numbered harmonics. The second mechanism is horn loading, which reduces excursion in the passband (above 30Hz), which in turn reduces distortion above 30Hz. The third thing is the front chamber and horn folds provide a low-pass filter that attenuates high frequencies, and that results in a reduction of harmonics from third on up.

The difference in output is about 15dB too. While that's not an indicator of quality all by itself, the fact remains that you need about 50x the power for the three π to equal the output of the 12π. So the 12π is loafing where the three π might be nearing its limits.

The three π is tuned lower, so that's the one area where it will perform better. You'll get flat response down to 20Hz. It is also a much smaller box.