If there is no specific reason to do otherwise, try to set the "Show on Stories" fields of these intersecting Walls to "Home Story Only". Then you will not see the missing Wall pieces at their intersection.
The reason you see them currently is because their intersection is calculated in 2D since the upper Walls hang down into the vertical range of the Story below them (because their "Show on Stories" field is set to "All Relevant Stories", the default value). Thus ARCHICAD calculates the 2D intersection between the intersecting Walls, in which case one Wall crosses the other and this shows on their 2D as well. The upper Story Walls are not visible in the lower Story because they are above the Floor Plan Cutting Plane, but their effect on the 2D of the intersecting Wall is visible.
As far as which intersecting Wall cuts the other: I think in case their Building Materials have the same Intersection Priorities: the one created later will cut the other. Later modification of either intersecting walls does not change this based on my test. Only if you Cut (CTRL+X) a Wall from a project, then repaste it (CTRL+V) will change this, because then the Wall instance is deleted and the pasted instance will be count as a newly created instance. With this trick you can influence which Wall cut the other. At least it works for me. (But this is just a trick for future reference, setting the "Show on Stories" fields to "Home Story Only" will solve your immediate situation.)
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