They will equip the armor that gives them their best protection, given their skill set and perks.
I don't have any Blades Followers so I have not tried with them. However, after spending time with enough followers, I stopped worrying about getting them fully protected.
Followers unequip the armor you give them when you dismiss them and you (or they) leave the cell. They reequip it again when they start following you (under certain circumstances, I usually trade one piece with them and they reequip the whole set). They also occasionally get a duplicate set of their original gear as a result.
It's annoying, and probably a bug.