So... I'm looking for a +2 weapon

[Thump]

and I decided on a large +1 Falchion, but I can't decide if I should put Keen or Corrosive on.

I'm making an antipaladin for a campaign my friend is hosting, and one of the items I picked up was Strongarm bracers so I could use large weapons. We also houseruled in that antipaladins don't have to be CE, they just have to be any evil alignment.

I've picked Lawful Evil, so what would a half-demon tiefling antipaladin end up using, between Keen and Corrosive? (or any other +1s)

[Eldest]

I generally prefer Keen, as I like crits. But really, that's just my nonoptimized opinion. Somebody will come along shortly and tell you how to make the ubersword.

[Big Fau]

Corosive, hands down. Keen is better purchased through a Scabbard of Keen Edges (Keen Weapon 3/day, which is enough to last you through most encounters) or in a wand (and using the Wand Chamber option in Dungeonscape).

[Thurbane]

Corosive, hands down. Keen is better purchased through a Scabbard of Keen Edges (Keen Weapon 3/day, which is enough to last you through most encounters) or in a wand (and using the Wand Chamber option in Dungeonscape).
Or a Wand of Heroics, to get Improved Critical (you'll need BAB +8) - it's a second level spell, and so cheaper than Keen Edge, with the same duration (assuming same caster level).