BOSE Sub 1 vs Behringer B1200D laggy subs?

I have both Bose Sub 1 and Behringer B1200d. The Sub 1 seems to have a slight audible delay on the low end beat when compared to my Yamaha Stagepass 600 top boxes. Especially noticeable when kick bass drum is not aligned with a sidestick. I am very sensitive to this as I use this set up as a backing PA system while I play live music. The Behringer is not as deep, but the bass drum sound hits tight on time. Is this due to some sound processing lag in the BOSE, or the Behringer's higher efficiency, or maybe the BOSE is trying to move more air at lower frequency, which has more inertia. Feels like a phase alignment that is just a few milliseconds out.

By the way, I connected both subs to the "sub out" on the Yamaha mixer board ( one at a time), as the top speaker boxes are passive, and must connect to the mixer board for power. I can then match the Behringer sub cut off to the Yamaha's mixer board 120hz cut off, but cannot do the same for the BOSE Sub 1 as it has no variable cut control - it is expecting a BOSE S1 Pro or L1 system for mid/upper range. As a result, I do not run the Yamaha Stagepass top boxes through the subs like normal powered top boxes - which means any DSP signal processing or cut off from the sub is not used in the top boxes.


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It is possible the Bose has some processing delay built-in and for subwoofers group delay is higher the lower they go. There is no fix for either of these besides physically positioning the Bose sub ahead of the mains to help time align them better.
 
I know some subs have an engineered delay for any powered top boxes connected through them - I have seen this in the RCF Sub 702 in the LCD menu
BOSE would most probably fine tune this delay to their own set ups too, so that any array was perfectly time aligned to the slower moving subs. I doubt that the Yamaha Stagpass 600 has the sophistication to delay its top boxes when a sub is connected - they could not know the delay specs on the sub. The delay would become more obvious the lower the frequency the sub is, and would be even more obvious with less efficient woofer cones that take more power to get moving. Most probably explains why the Behringer B1200d is a better match to the Yamaha Stagpass - it is a much more efficient, lighter bass cone, and does not go quite as deep. Therefore much less delay in the kick drum. Just my thoughts.