The "dimensions" that "scale properly" are not Dimensions at all, but independent Mtext and Line and Hatch pattern pieces, so of course they scale as any plain objects do.
The actual Dimensions that don't are behaving as Dimensions do -- they follow the definition of a Dimension Style [though these have an override on the Text Style used], and sizes of elements are based on the effective Dimension-element scaling, etc. If you really want to have Dimensions for different-scaled drawings within the same drawing file, you need to give them overall scale factors appropriate to the scale of their part of the drawing.
In your case, if you change that overall scale in the reduced one to the inverse of 25.4 [in the Properties palette, Fit category, Dim scale overall slot], its parts will be sized appropriately. You also need to compensate for the difference in the actual measured length, since you shrunk that, if you're going to show a length instead of your override non-numerical text. That's already compensated for in the big version [the inverse of 25.4], so for the one in the small version, in the Primary Units category, change the Dim scale linear value to 1.
Kent Cooper, AIA