So the cubic inches lost is 154 less the space taken up by the internal mechanism. How much is that?
Suppose the handle and wheels each take a 1inch by 1inch space at the top (9 CI each). Suppose the tracks are each 1 inch by 1 inch along the whole height (22 CI each). That makes 62 CI total, and I think that all of the above assumptions are too high. Still, the difference is 92 cubic inches.
But I'm confused about your sketches:
Suppose that we have a box with the external dimensions. And we have the same wheel & handle mechanism. Clearly, the sides are in the same place, the top is in the same place, the only question is do you put the "bottom" above the mechanisms, or below? Since we started with the same box the external space is the same. And the space difference is obvious. The only variable that might be different is if B&R designs the mechanism differently because it is on the outside.
Note that if you talk to bag designers the standard way to measure bag volume is to fill it with 3/4" balls and count them, not to calculate volume.
But it's easy to come up with ways to measure usable space to give whatever answer you want. For example, if you are filling your bag with rigid sheets that are 22X14, the B&R bag holds more, since the mechanism conflicts.