Heavy Armor: Seems like the best armor style, right? Not necessarily. Heavy Armor may provide the highest armor value in the game, but the armor itself can be a burden. For one, it's weighs a lot. It costs a lot of points just to carry the armor much less wear it. Secondly, it slows you down. You may need to be able to get out of something and you have no speed to do it. Of course there's a perk that lets you wear it for free and doesn't slow you down, but you have to use two perks to spend on things you don't really need.
Heavy Armor works best if you are using Two-Handed Swords and Dual Wielding two swords for an extra armor benefit to compensate for not having a shield.
Light Armor: A mobile warrior can be more fearsome than a strong one. Light Armor provides the warrior enough armor value to live through fights, but it doesn't do enough on it's own. When you're wearing Light Armor, you need a shield and know how to use it effectively.
If you're choosing to be a warrior, as long as you know the mechanics of blocking, you won't even need Heavy Armor. The blocking by itself can filter out enough damage to survive a fight with 3-4 enemies even when you're playing on the hardest difficulty.
Mage Armor: The problem with this armor is very present. Technically speaking, it doesn't exist, it's just magic on a timer. Mage armor can last between 1-4 minutes depending on your perks. If your armor turns itself off, you are almost surely doomed to die.
On a brighter note, the only people who use mage armor are mages. Mage armor is nice because you can wear your original clothing without suffering mobility or weight cost. Even so, if someone chooses to wear Heavy Armor, they can even get the benefit of up to 80% damage taken off of them while still wearing Heavy Armor making them almost unstoppable.
Anyways, those are my thoughts on the three armor types.