How do I compare armour pieces for my companion?

Solution 1:

There is no way to view companion armor in the same way you view your own.

However, armor has relativley the same effect on your companion, as it does on your player character.

A viable option would be to take the original armor from your companion, equip it, and compare other armor in relation to your player character.

Also note that fallout uses a base assumption when displaying armor as an upgrade. Depending on your playstyle, a percieved "upgrade" may not necessarily be an upgrade, as base values are compared, but not secondary effects.