Companion: Ember
Abilities used: Starfall, Crystal Blast, Sniping Silver, Shocking Burst, Destructive Blast, Haste, Second Wind.
Equipment: Ice Staff, Light - Aggressive, Shattering, Quickened. Medium - Shattering, Quickened.
Target: Skeleton sitting on throne in Bonesnap Ruins Public Dungeon

There are no Target Dummies that companions can reliably test on since they aren't allowed inside player homes except as a houseguest NPC. There is a Public Dungeon in Stormhaven where the skeleton sitting on the throne can be attacked, dropping an AOE effect on top of it causes your companion to attack it. It does appear to have the standard armor value, has infinite health, best of all it is stationary and doesn't attack back. Medium I tried with a full 5 list of attacks as well as with 4 attacks and Second Wind, honestly didn't make too much of a difference. However, going with Light and using Haste to change from 5 to 8 attacks did considerably more damage repeating every 37 seconds or so. If you're wondering does Haste and Second Wind work on each other, YES IT DOES, Light - Quickened I was getting Haste to cast every 15 seconds as 2 casts of Second Wind kept shaving off 10 seconds and Haste reset what remained on Second Wind.

I didn't use any player aided buffs or debuff the target in anyway, it was purely the companion's own abilities, if you were to apply Major Breach, Minor Breach, and Crushing to the target then Aggressive and Quickened would have done full damage; however, the enemy I'm hitting can't be directly hit by players only indirectly from ground effects or splash damage. It's not possible for me to hit it with Pierce Armor which would otherwise bring its Armor to near zero. In most situations when using a companion, are you applying maximum penetration to your target is something to consider. I also don't have any addons to track the timestamps of the companion's attack rotation, I would need someone else to do that so all I have for now are the numbers. If you must know, with Shattering or Aggressive your companion will auto-attack 4 to 5 times before the next ability rotation with another auto attack before Sniping Silver. Quickened they will auto attack 2 to 3 times before the next rotation. And finally its a total blur when you have Quickened, 3 abilities, Haste, and Second Wind that looks like a 9-chain consecutive abilities with a slight delay on the last action every 15 seconds. In the long run 9-chain is awesome because it uses Haste and Second Wind more frequently, but only Ember can utilize this.

Why didn't I test Medium - Aggressive? The most expensive was Light - Aggressive and that cost in total 1.5 million gold, Medium - Aggressive even at the cheapest items available will run me around 60 million gold which I don't have and being a solo / guildless player will never have. If you want to donate some funding you can send it to @phane480 on PC/NA know that I won't be able to pay you back, but I won't spend it on anything other than Medium - Aggressive to test... and keep.

TLDR; Here are numbers.

Light Armor - 19.5% Aggressive
Light Armor - 9100 Shattering, 7.6% Aggressive
Light Armor - 31% Quickened
Medium Armor - 9100 Shattering, 7.6% Aggressive
Medium Armor - 31% Quickened