Comparing a quaternion to a contact point normal

I'm using the NewtonVR package for object physics. One of the classes, NVRInteractable has a standard Rigidbody. I'm attempting to compare the angle of object A with the contact normal when colliding with object B.

More specifically. I have a box and a sword. I'm trying to create a slashing coefficient (blunt edge does much less damage than the sharp edge, about 0.2-1 with a curve that I'll define mathematically) by comparing the rotation of the sword to the contact normal generated by the collision with the box.

I tried normalizing the quaternion and comparing the two since the contact normal is already normalized but I was getting numbers well outside of the normalized range. I also tried getting the dot product of the two but I was similarly getting a very odd set of numbers.

Was I right to try this? Should I be tackling this problem with some other method?

Thank you for any help!