I think it's dependent upon what type of garment. I do believe that Fed enlisted mounted shell jackets used 1/2" tape for their trim. Where the frocks were using the smaller 3/8" piping for the trim.
Not sure if the original question was to source tape for a project but just in case...
AFAIK the correct trim tape should be wool, not cotton. (Most of the tape sold in stores is cotton.)
If you are talking about the width of the welt on officer pants, that's rank. Other measurements on rank are also determined by bullion length on epaulettes too. Shoulder boards as well have 1/4 inch measurements on the borders as opposed to 3/8 post war