Well, I usually I don't pay much attention which class is "overpowered" and which are not, and just playing whatever class I like. But after reading several similar threads I decided to make some kind of test - kill two dragons (High Abyssal Dragon from quest and Hinterlands one, both fire).
My party was level 16 - melee Assassin Inquisitor, Varric, Cassandra and Vivienne. I geared into loot and quest items mostly because I only have one Tier 3 craft recipe (my rogue dagger) and have very little Tier 3 crafting components. So, I assume my team has more or less "average" gear. I also had some Fire resistance belts. Potions was standard Healing, Regeneration in second slot and almost fully upgraded (except AOE effect) FR in third.
Inquisitor is pure offensive dual daggers/stealth/assassin spec without any survivability talents but Stealth (I usually babysit him in combat).
Cassandra has 4 points in Templar tree (Improved Spell purge and Blessed Blades), the rest is distributed between Shield and Sword and Vanguard trees.
Varric's skill points distributed evenly between ranged combat and artificer trees.
Vivienne is specced to KE (full tree except last talent) and Spirit (full tree except Revival). I didn't spec her to more offensive because she is the only mage in my party. Anyway, all KE haters says that it is "one-button spec", so we probably don't need any offense but Spirit blade, isn't it? 
So, I attacked Dragons, and...
My rogue can't survive long enough in both fights. He just haven't right build, i think. So I let it be killed.
AI controlled Varric can survive for some time in High Abyssal Dragon fight, but can't survive in Hinterlands. Since his survival wasn't my goal, I let him die and raised him occasionally when I had time to provide some additional damage.
Cassandra... oh yes, baby. She could survive both fights on her own, with minimal manual intervention.
And our KE, Vivienne. I controlled her almost exclusively in both fights. She hasn't died and dragons has been killed eventually, but it was nothing like "press 1 button to win". It required a lot of micromanagement. Even with all my talents for Barrier, it can't be maintained between cooldowns in the fight in Hinterlands, mainly because attacking dragon with Spirit blade provides almost no barrier. So without tanking Cassandra I would be doomed for certain. High Abyssal dragon is another story - he has Guard, and Spirit blade really shines here. Anyway, KE DPS with Spirit blade is really bad, so both fights also required considerable amount of time.
So, if we speak about who is "overpowered", then Warrior, not KE should be first target. Cassandra is basically undergeared generic warrior tank with four talent points wasted (her Templar talents didn't help much here), and still, she could survive both fights tanking dragons while AI controlled! I wonder what properly specced Champion can do... KE survivability is good, definitely better than generic rogues
, but I wouldn't describe it in the way "I steamrolled anything with just mashing Spirit blade button lol".
Yes, probably I can tune up KE spec for solo combat, get better gear, and so on... but it also true for many other classes. I definitely sure that warrior is not worse, I read about rogue archers soloing entire game, and so on. So I don't understand why KE is specifically marked as "ovepowered" by people.
Also I assume that there can be some basically invulnerable characters exploiting "guard on hit" mechanics on gear and talents, but again, it's not KE specific.