Comparison of Two 3D Models to Determine Orientation Difference

Question

I am working on a project where I am trying to compare a 3D reconstructed model with a predefined 3D model of the same object to find the orientation shift between them. An example of these types of models can be seen here: example models.

I was thinking about maybe trying to use Kabsch's algorithm to compare them but I'm not completely sure that will work because they don't have the same number of vertices and I'm not sure if there's a good way to make that happen. Also, I don't know the correspondence information - which point in set 1 represents which point in set 2.

Regardless, I have the model's PLY files which contains the coordinates of each vertex so I'm looking for some way to compare them that will match up the different features in each object together. Here is a GitHub repo with both PLY files just in case that would be useful.

Thanks in advance for any help, I've been struck trying to figure out this problem for a while!