There is such a thing as a Raleigh's constant, but it has nothing to do with Pinhole photography:
I think what you're referring to is simply the square root of the Airy disc's diameter (square root of 2.44 or 3.66, respectively). One maximizes sharpness (2.44). The other maximizes resolution (3.66).
You correctly referred to the angle of view, which is calculated from the negative-format diagonal and the focal length, but we need to make sure that we are not confusing it with the 'actual' angle of view, which is highly dependent on the thickness of the pinhole material and responsible for the image circle? (see attachment)