Playing one way verses the other has some effect, but not what people think.
The woofer itself, meaning the motor structure and frame, will take up some air space. So the amount of compression on one side verses the other side is different. So flipping one woofer around equalizes the pressures.
So have claimed it can cancel out some even order distortion, but that is still almost theoretical at best. Measuring any distortion outside of an anechoic chamber is nearly futile. Room noise levels typically exceed the levels actually being measured.
It is like measuring the level of one persons voice in a crowed room among a hundred others.
You can move the microphone close to the speaker to change the differential, but rest of the room noise is still in the response.
So it is like moving the microphone closer to the one persons voice that you are trying to measure while the rest of the people are still talking.... It is still a mess.
To measure any real effect (if there is any) one need to be far enough away for the woofers to sum as a single unit. And you again can't really do that and get any meaningful distortion measurements outside of an anechoic chamber.
And on top of that, distortion is really nothing. By that I mean it is a drop in the bucket compared to the settling time of a woofer being played hard. That is where real audible differences take place and where the servo control system really sets itself apart.
Another myth involved in flipping one woofer around is that there is some kind of force cancellation. That is not true. When a woofer is flipped around you also flip the polarity on that driver. So it still moves in the same direction as the other woofer. So all of the force is moving in the same direction.
Flipping one does separate the acoustic centers a little bit, but the wavelengths being played are so long that it doesn't matter too much. Even at 200Hz the wavelengths are still five feet long.
I have a related question about the OB subwoofers. How much does the H or W frame contribute to the sound? If you were to mount the subs on a very thick baffle (similar to Spatial products), without the H or W frame, would you be giving up very much? I'm guessing they might not go down as low in frequency. Giving up a little there, as long as it wasn't too significant, might be worth it aesthetically.
The H frame and W frames allow greater separation of the front and back waves while also loading the drivers. This extends the low end response and allows for more impact.
A flat baffle allows cancellation to occur much more quickly reducing output and extension.