The Ideal Gas Law is PV=nRT where P is Pressure V is Volume, n is moles of gas, R is a constant and T is absolute Temperature.
Assuming all else stays the same, the difference in pressure would be the ratio of the volumes into which the gas expands which would some cylindrical space, PiR2XL or Pi times the Radius squared times the length of the space. In this case it would just be the ratio of the Radius squared of the 12 gauge bore to the 10 gauge bore which works out to be 94% reduction.
One can threfore understand why a measuring device may show no difference.-Dick