>Armstrong or Billings
Given only that choice, I would lean toward Armstrong.
Billings virtually never used raised text on wrenches, except on one carbon steel series in the 20's, and that has thick jaws.
Armstrong on the other hand often used raised text, and often made wrenches with very deep openings in them, including wrenches made in the 40's....
Having said that tho, I know of no Armstrong wrench that looks quite like that, particularly the style and location of the fractions. I have seen very few examples of Whitworth wrenches from either tho...
The other odd thing is, assuming it is armstrong, the rough finish would indicate it is a vanadium steel series, , the later chrome-vanadium wrenches were smooth between the ends, but the date range transition should be the late 30's....