Neither, and I'll explain at the end

Seriously though, if you were stuck between the two? Short term? I'd probably go with the faust if you want to get some curst resist to use it's charge attack. It's great for farming Jelly king till you get sick of this game. Long term? Go with the Avenger, you will often be soloing T3 for mats and the like and you want quick kills from construct and undead which means using the charge attack. They are decent swords but in T3 a lot of situations call for faster weapons that allow you to cancel and shield.

As for the calibur? Once again neither. But in a force? Well Cold Iron Carver leads to cold iron vanq which gives you extra undead damage, but if you have an avenger why would you be using a cold iron vanq in the fist place? You should have weapons that exploit all enemy weaknesses by T3 instead of having an all in one weapon. Ascended Calibur is also great if you are either on a budget or if you just like the 360 AOE knockback. That is where it shines, it is a room clearer allowing you to move around if surrounded like arena.

But with the latest arsenal expansion I find that the new weapons are superior compared to the old weapons and if you are willing to get a third weapon slot then you can pretty much be ready to take on any mob in the game.

Flourish series- I prefer this series over flamberge and rigadoon because in terms of raw damage it is just great. Destroys beasts and fiends easy and that charge attack is godly which you will be using a lot if you solo T3. Raw piercing damage that is also oddly enough great on the gremlins.

Fire brandish series- It is really down to preference and I bet the glacius would be better in vanaduke to counter oil slimes but overall I love the fire brandish series. Strong fire means that your charge attacks will whittle down construct and undead even when you aren't attacking. Great against lumber mobs and doing graveyard T3 runs.

Nightblade series- Shadow wrecks jelly mobs and gremlins and while doing JK runs Faust is superior given the raw number of jelly mobs they throw at you. However, once you are out of JK runs you won't be fighting much slimes where it will be more of a small group vs you and nightblade will do just as much damage as that faust but quicker. I really don't worry about the curse from faust but that's because I have a suit of armor of curse resist so I don't get cursed but nightblade does allow you to use that charge attack a lot more.

Once you get the 4* weapon of each of these series you can pretty much make this game easy with some few exceptions(flame puppy+ oil slimes=RIP you). Just take your time and don't rush into battle head first and abuse that shield and you will reap the benefit without any consequences.