Sword of Kas was first published in Eldritch Wizardry. I don't have this rare booklet so for purposes of this treatise I'm starting with the 1st Edition AD&D version and moving onward. The Sword of Kas like many iconic things D&D related has continually changed over the decades and editions. Let's see how they vary (SPOILERS BELOW):
1st Edition Dungeon Masters Guide: Gary Gygax's version of the Sword of Kas starts it all off. The artifact is intelligent and has an overriding desire to kill Vecna and his cult. This is common across all the editions so let's call this "a given" from here on. In this book, the blade is a +6 Defender short sword with an 15 Intelligence and 19 Ego, doing double damage against non-Prime Material Plane beings. This is significant because no item in D&D lore is +6 anything until this point. The sword is also merely a short blade which is a major point of difference in the future. AD&D always allowed DM's to fashion artifacts to their own need, allowing them to choose from a list of powers and drawbacks. For simplicity, the Sword of Kas has 5 benign powers, 2 major powers, 1 minor malevolent power, 2 major malevolent powers, 2 prime powers and 1 side effect. These extras would be expanded upon more definitively in later publications.
Vecna Lives!: David "Zeb" Cook brought us the module that launched Vecna from mystery lich to major story villain. The Sword of course figures prominently in the adventure, but this time it is a two-handed sword. This is probably because fighters (like Kas we assume) are more prone to choosing longer blades unlike thieves who are suited to shorter backstabbing blades. Beyond length, Cook's sword stays fairly true to the AD&D version being a +6 Defender with a 19 Int, 20 Ego and double damage versus non-Prime Material Plane beings. He further enumerates the powers giving Immunity to Fear, Magic Missiles, Charm Person and Hold Person spells. The sword pollutes holy water and can cast Foresight, Plane Shift and Shield plus grant Fire Giant Strength and Paralyze foes limited times a day. Cook gave the weapon a higher intelligence in my opinion to better outsmart the fighters holding it. The sword's drawbacks are devious, it needs to be sated with blood daily or it tries to take control and second the sword shuts down within 60' of Vecna or his artifacts.
Book of Artifacts: David Cook also wrote this AD&D manual and the sword is again here in a similar fashion to Vecna Lives!: +6 Defender, 19 Int, 20 Ego, holy water corruption, Foresight, Shield, Fire Giant Strength, no Paralyze touch, and 3 random immunities and 2 random major powers. Gone is the double damage to "outsiders" and the sword gets nastier doing 2d20 damage when first touched among the usual shutdown drawbacks. Also gone is Plane Shift, never to return.
Die Vecna Die: This 2E module tries to put Vecna down for good and authors Bruce Cordell and Steve Miller put their own spin on the sword: +6 Defender short sword (why?!) with Foresight, etc. etc. however there is no Fire Giant Strength 3/day. This time sword gets an upgrade of Fire Strength, plus immunity to Fear and Paralyzation only if the wielder also has the Eye or Hand of Vecna. Seems excessive and contrary to the sword's theme, but okay. The cursed sword also only deals 2d10 damage on first touch, I guess 2d20 was killing too many candidates.
3rd Edition Dungeon Masters Guide: Monte Cook, Jonathan Tweet and Skip Williams had to include this famous artifact in their new edition of D&D and their version is more streamlined and fighter friendly: +6 unholy, keen, vorpal, long sword, granting +10 Strength. This is the first time the blade is a long sword and vorpal. The keen kind of takes care of the double damage lost during 2E, but the continuous giant strength boost is over the top with everything else already included. It is dumbed down, 15 Int, 13 Wisdom, 16 Charisma but a whopping 34 Ego. It has some new tricks too, casting Call Lightning, Blasphemy, Unhallow and Slay Living.
Open Grave: 4th Edition's supplement, Open Grave by Bruce Cordell , Eytan Bernstein and Brian James continues the legacy of the sword and with the new rules-set the blade gets quirkier yet: Now it becomes a +5 vicious short sword (of course) with a 5d12 damage critical. It deals even more damage to allies (2d10), grants +5 during total defense (naturally) and among its weirder properties (which I won't detail all them because they're pointless) it is invisible until it strikes a target and even does +5 damage to Vecna and his cultists. The sword gets various upgrades which I won't get into except one, anyone who possesses both the Hand of Vecna and the Sword of Kas deals a 5d12 crit on every hit against Vecna or his gang. That's a major reversal for an artifact that at one time shut down completely in his presence. It was the whole point of Kas' failure to slay his master with the sword. Will 5E redeem the Sword of Kas?
5th Edition Dungeon Masters Guide: Jeremy Crawford, Chris Perkins and James Wyatt's chance at the sword goes like this: +3 long sword, 19-20 critical, extra 2d10 damage to undead. It has 2 random properties and 2 random drawbacks. It has a 15 Int, 13 Wis, 16 Cha. The sword's bonus is scaled back like much of the edition's combat, but I see it's still keyed to killing undead things like Vecna. At least there is no vorpal properties or fire giant strength boosts. The sword adds d10 to initiative and the attack bonus can be put towards AC. That's the old Defender ability with a new twist. Spellwise, it has Call Lightning, Divine Word, Finger of Death. The sword still doesn't lose it's power when facing Vecna or his items so the futility of the sword's purpose isn't as bad as in the old days.
Well that's all for now. I'm sure with all these factors in one place one could distill the properties of an average Sword of Kas with general D&D rules. Strangely if I had to pick one version I'd go with the Vecna Lives! one because it's setting canon, but hey that's me.