Along East University Avenue (IA 163) in Des Moines, the street signs for the various side streets the road intersects are green signs with rather big type, whereas the signs for University Avenue itself are blue signs with much smaller letters (as shown in this picture (https://www.google.com/maps/@41.6006982,-93.540602,3a,37.5y,315.72h,95.07t/data=!3m6!1e1!3m4!1sXgYLSxfqv_VKiOKbdya3Ug!2e0!7i16384!8i8192?entry=ttu)).
Throughout the country, where else have you seen an intersection where one of the street signs has the street name printed in a much larger font size than the name on the other sign - especially ones where, as in the Des Moines example that I posted, the sign with the bigger typeface is the one for the more minor or less important road?
I would think that the signs for the minor road being bigger are more common. SH-9 in the east part of Norman, OK has such an arrangement, with cross streets having larger blades than the ones for SH-9 itself. That's because the speed limit on Highway 9 is in the 50-65 range and the cross streets are generally at 45 or lower. So it makes sense to have larger signs facing the high-speed traffic on the main highway.
In some places in NY, it's becoming common for the more important street to have a smaller sign on top of a large blade for the intersecting street.
Huntsville, AL, does it for the side/cross streets at unsignalized intersections along the arterials, such as here (https://www.google.com/maps/@34.7072376,-86.57093,3a,15y,55.11h,89.5t/data=!3m6!1e1!3m4!1sT8aBxV5_DdOdiZMWYpUQPQ!2e0!7i13312!8i6656?entry=ttu), though it honestly makes sense given that the arterials are generally a lot larger with a higher speed limit than the side streets, so you'd want the ability for drivers to be able to see the side street names from a greater distance off.
This became the standard for new street name signs in Clarke County (Athens) GA about five years ago, wherever a major arterial/collector intersects a local road. I'm not sure I'm a fan of it (I would rather see all street name signs in the standard sizes).