If you're comparing a small film-format pinhole image enlarged to the same size as a large format pinhole image, you will see enlarged pinhole artifacts in the enlarged image. For one, the image "blur" will be enhanced by the enlargement factor, such that an f138 pinhole image enlarged 4x would give an apparent blur in the final print equivalent to (138/4=34.5) shooting a f34.5 pinhole in the larger format camera directly. However, attempting to compensate for this enhanced blur in the final print by using an abnormally small pinhole in the f138 camera merely results in more diffraction in the image, if the abnormally small pinhole is smaller than that recommended by Rayleigh, et al. The net effect is that larger film formats will have intrinsically better sharpness characteristics to the image if optimized.
MkII, your suggestion of a larger format camera with the f140 aperture actually sounds reasonable, because in the real world of practical pinhole photography the exposure time can affect image sharpness at least as much as absolute aperture, due to subject and camera support movement, plus the problems with compensating for reciprocity failure at these extended exposure times.
I understand that Fuji Acros has improved reciprocity characteristics over more traditional emulsions like FP4, so you might want to give that a try, for reducing your exposure times at smaller apertures.
There's also a certain crossover point where paper negatives end up giving you shorter exposure times than traditional film, since, although they have an intrinsically lower base ISO, exhibit virtually no reciprocity failure.