3D rotation mismatch calculation

I am trying to figure out a way to compare the 3D rotation of two objects and find a measure of HOW MUCH they are mismatched. The only thing I have is I have the two objects' matrices or quaternions. Is there some way to say how much their rotations differ?

The reason I need it is because I'm comparing two methods to rotate 3D objects and experiment participants have to rotate an object to match a target. i.e. I need a way to quantify the mismatch.

Any advice would be appreciated.

Jubei