Well, in my humble opinion things are a bit messy here both because of David's will, both because there is an excess of variety in this game that is not 100% intentional.
Among the 2-hand weapons, I use:
Cruelty as main weapon for many circumstances: it deals a higher DPS than any axe (not to mention the vicious bonus) and has a huge elemental damage that is augmented while striking a lot of foes, from animals to undeads.
Souldrinker vs. enemies that are resistant to fire and vs. animals. It is even better than the Great axe of falling Stars because, even if it has "only" Beastslayer 1, it compensates the +2 damage from Beastslayer 2 owned by the GAOFS with a +1 basic minimum and maximum damage and a +1 death damage, resulting in short in a more versatile weapon dealing the same damage to animals and more to non-animals. Maybe the only exception is given by vorators, that are still beasts, but then I prefer to use shock weapons that are even more effective.
Executoner's Axe is a great weapon but overall inferior to Souldrinker. I keep it in case that it may be enchanted one day, and vs. golems that are unaffected by any magical damage. It is a close call with the Bone Maul that deals an impressive average basic damage, being A LOT better than Gurgurth's Maul .... maybe even too much. David, are you listening? How can a common item being so better than a unique item?
The Maul of Garrak is a great weapon too, but the Boots of Stability are such a "must have" that I have never chosen it as a valid reward.