I think they only compare when the piece of equipment you are looking at is of the same type as the item presently equipped to your player. Like you have to compare a one-handed axe to another one-handed axe that is presently equipped for it to show up. Like when I try and get the red/green comparison between a two-handed sword and a single-handed axe, it doesn’t show up.
I have at least one companion and haven’t noticed it change....... yet.