Do they really look the same size? The moon itself doesn't even look the same size consistently. Some nights it looks gigantic. I can't even look at the sun long enough to tell what the definitive size of it is.
Regarding seeing gigantic moons, I know what you mean. There is a weird psychological effect where objects, particularly the moon, look bigger near the horizon than at the top of the sky that is apparently in our heads and not due to any physics of, say, refraction. I've tested this for myself by pinching a large moon between my fingers and watched it visually then suddenly seem much smaller.