Among the 'Big 3' unique Legendary melee weapons that are relatively easy to get - Grognak's Axe, Pickman's Blade, and Kremvh's Tooth - which is objectively best? Which does the most damage in the shortest time? Heck, add Big Jim into the conversation if you want. Any other very powerful uniques I'm missing?

(And yes, I know that the Kremvh's effect can be moved to another Legendary for an even more devastating weapon, but let's consider the vanilla for now since it can be reliably acquired without luck getting random legendaries.)

I simply have to use Grognak's because I'm playing a PA run, and a little knife would look stupid, but is the Blade really twice as effective as the Axe?

i have to admit, i have pickman's, but i have a similar weapon, combat knife, that i have crafted that works better, for me at least.

PIckman's Blade got me a lot of mileage, especially using VATS. I'd put my money on Pickman's because of the double bleed (one from legendary effect, other from stealth blade) that stacks with each hit.

I haven't experimented much with Grognak's, so hopefully someone more knowledgable can fill in the gaps.

Grognak's

The niche for this weapon is that it is a heavy weapon that functions like a medium speed weapon. The swings cost less in vats than other two handed weapons. There is a hidden legendary attribute that increases stagger chance, but I do not know if it is the same as the standard legendary title, of if like Shem Drowne's sword, it is a lesser effect than the standard. Its biggest disadvantage is that it cannot be modified, so only melee and related perks will affect its performance.

Kremh's

As it stands, it will outperform the vast majority of legendary random drops that you would find, overall, but is itself outshone in some ways by other legendary/unique weapons. But... there's a bit of a hidden trick to Kremh's. Like Lorenzo's Artifact, the unique nature of the weapon is not a legendary attribute, but rather a unique mod. And, like Lorenzo's, the mod can apparently be removed. It can then be inserted into another Machete. If that machete is a legendary one, the final result will have the effects of the Kremh's mod, as well as the legendary trait. I do not know if the mod can be infinitely removed and placed in new machetes, but from what I read it is possible to change the legendary attribute by removing it and moving it to a new one. Obviously, this allows Kremh's Tooth to have ability combinations that would make it objectively superiour to almost any other choice, depending on the legendary attribute.

Pickman's

Pickman's can be modified, but it is unwise to do so, as the existing mod is the best one for it (as far as I know, it always comes equipped with the "stealth" mod.)

Pickman's ability is one of the most powerful ones available to a Fast Swinging Melee Weapon - Bleeding. Unlike poison or incendiary, the bleeding effect applies its DoT very quickly, and it stacks with itself. That means that repeated strikes with Pickman's do a lot of stacking damage. It also works very effectively as a stealth weapon. If the initial attack fails to kill the target or stealth is lost, the AP cost is low, so repeated fast strikes are still effective against targets that don't have huge health bars.

Personally, I pick Pickman's. I play a stealth character, so it suits well. Also, the only Legendary Machete I have is a Sentinel, and I don't see 15% DR from not moving being all that useful to a melee character, so I'm holding out for something better before I play around with Kremh's.