Both sides provide Light and Heavy armor. Right side provides all Heavy and ends with Light, while left side provides all Light and ends up with a Heavy. Dragonplate Armor is weaker than Daedric Armor, but it's irrelevant as you can reach maximum protection even with Steel Plate armor, so obviously Dragonplate will be enough as well. So there's no real advantage going right side, armor-wise.
It's weapons that make the difference. Without Dragon weapons, the best weapon class available to left side is Glass. It is worse than Daedric. But how much worse?
Here are some of the damage values. First is glass, second is Daedric.
Dagger - 9/11
Axe - 13/15
Mace - 14/16
So the difference, as you see, is pretty small - 19% damage in case of the dagger, 13% in case of the Mace. With higher numbers(2H versions) the percentage will decrease further.
But these are unupgraded versions. What if they're all Legendary?
Dagger - 19/21
Axe - 23/25
Mace - 24/26
Since upgrading applies a flat, linear bonus no matter the weapon's initial damage or type, this drastically decreases the damage difference between weapons. The Dagger differs now by only 10%, and Mace by less than 8%.
So going left side instead of right you save yourself one perk point, still have maximum possible armor damage reduction, have a weapon that's way easier to upgrade(no Daedra hearts), at the cost of less than 10% damage difference.