Greatsword has ~10% more base damage on its light and heavy attacks, has a slightly higher attack speed (at least it says so in armoury, although it feels more equal or slightly slower than executioner with heavy attacks), 3x more damage cleave and ~40% higher stagger cleave. It has the rare and unique property of Heavy Linesman, which gives it the ability to hit several elites with over heavy strike. It can cleave into 4 Chaos Warriors with Mercenary and do damage to all of them, same with Stormvermin, and can cleave even more maulers. Heavy Linesman also has better modifiers against Chaos Warriors (CW’s will always 100% stop your executioner cleave swings) and other enemies like raiders and shields (Heavy Linesman cleaves them around 10% easier). It also has a push-attack that deals solid armour-piercing damage. It has also quite significantly better dodge, with one extra dodge count (3 is 50% better than 2, and is very noticeable) as well as 10% dodge bonus.
Executioner has significantly better single target elite damage with its heavy attacks, innate crit chance on heavy attacks and a bigger headshot damage multiplier which gives it higher potential and realistic damage. Tank property also makes it so the executioner has a stronger stagger effect.
Greatsword has significantly higher cleave, executioner doesn’t even compare. While executioner has significantly higher single target elite damage, greatsword can hit several elites with one swing, and while individually the damage is not high, the aggregate damage is quite equivalent, not to mention that it has a minor stagger crowd control effect. Greatsword also has the push attack for single target elites which pushes it up into average/below average single target armour DPS. Executioner is good at killing hordes, but in higher difficulties like Cataclysm+, the greatsword begins to shine significantly more, since the executioner is far more likely to stop it’s swing midway through the horde, stopped by a Chaos Warrior or 2 maulers, shields or Stormvermin, while the greatsword will keep going. It is superior to killing hordes, and the bigger they are, the better, while executioner suffers more. Executioner is also a lot worse at dodging, which is quite significant in my opinion.
The test conducted in this thread is absolutely terrible. It specifically portrays a situation where the executioner shines in (single target armoured elite) and the person didn’t even use greatswords push-attack. It doesn’t take into account that greatsword has significantly higher cleave (the highest in the game I do believe), that it can hit and damage several armoured elites, the better dodge stat and the great, reliable and simple heavy attacks.
I personally don’t get where this idea came from that the greatsword is this woefully weak and overshadowed weapon. Apart from the statistics that I’ve shown, I can also from experience say that I’ve used the greatsword a lot. It’s actually mt go-to weapon with Mercenary if I really want to win. I’ve brought it to C3O where it excelled due to the huge horde sizes, while the executioner wouldn’t even cleave a quarter of the hordes. I had several moments where I killed 4 Stormvermin with one heavy swing (of course that doesn’t mean I one shot them, but it still shows that it does damage, and as I mentioned, in total the damage is pretty solid). Now this doesn’t necessarily mean that the executioner isn’t better than greatsword. Maybe it is, and I certainly wouldn’t mind some tweaks to greatsword (the light attacks are not very good, I’d much prefer a fancier and more intricate light attack pattern, and a stab attack to follow the push attack), but I’m just saying that it’s not nearly as overshadowed as people think it is. It’s not cut and dry.