Aye, i believe companions have certain skills etc that rule what equipment they will use when given. Personally i would like them to be able to equip gauntlets and boots also. As currently only helmet, weps and armor will be used by companions.
What they will equip and use will depend on what they come with as default equipment and what you are offering them as replacements. I have Marcurio following me and I've upgraded his boots at least twice and gave him a set of gauntlets, but he came to me in mages robes so his stuff wasn't that great to begin with and I outfitted him in a whole new kit. I think that their weapons are controlled in the same way that weapons were controlled in FO3 and NV and it's mostly damage dealt. I've given him an enchanted bow and he equipped that over his default bow no problem. He also came with a dagger in his inventory that I can see and remove, which is awesome, and was unexpected, as I can control his combat that way, as he doesn't do melee because he has no melee weapon now, only a bow and his ranged spells that he casts.
@OP - I think the best solution in a mod would be to make all of Lydia's default gear playable.