Let me explain how I use Gimp software to compare dies in the difficult cases.
First we need two coin images that are exactly the same size and rotation.
I use Gimp on the Mac. After opening the image I use the Measure Tool to check the number of pixels and the angle between two things. For example I will use the tips of the anchor.
If the angles I wrong I use the Rotate Tool to get the coin into a close orientation. Instead of eyeballing it I type in the difference in angles into the Rotate Tool's dialog box.
Then I use Image->Scale Image… to get the two images exactly equal in size. I haven't found an easy way to do this with Gimp; I use Gimp's percentage scaling and cross-multiplication. For example if one image has 330 pixels between two points, and other has 300 pixels I will do 330*100/300 to get the percentage.
Then I use Image->Canvas Size to increase one image. Next I select the other image, and Copy, and select the image with the large canvas, and Edit->Paste as New Layer. The New Layer part is very important. I get an image like this:
If you aren't in the Rectangle Tool at this point enter it by clicking R on the keyboard. Then using the arrow keys walk the layer around until it is positioned precisely.
Then Save As. Choose a filename ending in .gif. Tell it to save the layers as animation with 1000ms between transitions.
Oops. Not a match. I had looked at undamaged places which were very close.
A match. Note especially all the snakes line up.
Hopefully you can see the obverses match and the reverses don't.
It is somewhat tricky with the obverses, because of the damage and the camera angle.
Photoshop software also has this ability, although I don't know the precise commands to work with layers in Photoshop.