I doubt very much that the 400 pushes more air than the 350v3 even at 20Hz. I've been struggling to understand how you heard more "kick" with the 400 compared to the 350. Are you sure it was the v3 350?

Now that I think about it thogh, the other thing that may have contributed to what you were hearing was the room. I suspect the 350 has a hump at 40Hz to 60Hz (and a corresponding dip up to 40Hz). Between 20Hz to 40Hz, room gain compensates for the 350 dip in smaller rooms. The 400 on the other hand has a flat response in these same regions due to DSP compensation. So if you were in a larger room, the 350's dip wasn't being corrected by room gain and the 400 therefore had more kick because it was flat.

So what were the dimensions of the room?

House of the Rising Sone
Out in the mid or far field
Dedicated mid-woofers are over-rated