I am expecting the apparent size of the earth as viewed from the moon to appear somewhat larger that the moon appears from earth considering that the earth is 4 time larger than the moon.

I think the term is “angular diameter.” (I had to look it up, as my space-word skills are rusty).
Try this, if it helps.
Yes, I do see the problem. It’s like I explained, since you can’t very well take a picture showing both the earth and moon side by side like that, how are you going to compare the apparent sizes accurately?
The only way to do that would be to take the photos under certain careful conditions, like taking photos from the earth and moon at the same time, with the same kinds of cameras and lenses, and making sure that you have some kind of landmark in both photos so that we have some means to judge angular distances. Just picking a random picture of the earth from the moon, and a random picture of the moon from the earth doesn’t actually tell you anything useful, since you are not making a scientific comparison and you have no context in which to judge most of the relevant factors.
Now, why hasn’t NASA or some other outfit done that? Probably because they all know the earth isn’t flat and what size the moon and earth are, so there is no actual knowledge to be gained from doing that type of exercise, so no scientist is going to waste their time and precious research dollars to do it.