Furious for me, every time. I figure I'm either going to take Keen or Improved Critical, and for that +1 I can snag one of them, or snag the other and pick up a +2 to hit and damage while I'm raging.
depends on how badly you need feats. If you do need feats, go with Keen. If you can afford Improved Critical (Falchion) as a feat, go with that.
You'll want keen after furious, as it's one of the best +1's, but Furious is extremely consistent.
Why is that?
The way I've used for calculating things like this is taking your results over the span of twenty rolls, one on each possible result of the d20 roll. In your case, say the falchion hit on a roll of eleven or higher dealing ten damage as it is now. When not raging, neither option would give you a direct, across the board damage boost. While raging, the furious weapon would pull ahead, by not only adding 2 extra damage on the ten hits you had before, but converting 2 of the misses to hits as well. This puts you at 100 damage in the keen case, but 144 with the furious weapon.
Of course, this doesn't count in keen's extra crits. Same example, but we'll take threats into account. You'd now threaten a crit on a 15-20, but you would have to confirm on the ones you rolled. Going off the "hitting on an eleven" basis, you'd be at about 50% of the crits being confirmed - 1.5 extra crits for double damage, on top of the 1.5 you get normally. Three crits puts the damage total at 130. The furious would threaten less often, but it would confirm those threats more while raging.
Admittedly, these are small numbers, where the multiplier on the keen doesn't fare the greatest. Same hit numbers dealing 20 per hit puts the keen to 260, with furious at 264(not including threats) while raging.
If you plan on doing a lot of fights outside of rage, or you're already hitting on rolls under ten consistently, keen pulls ahead. Otherwise, the extra +attack from furious gets you harder hits more often. This isn't even taking dice hate into account: how many threats do you roll when the monster is under fifteen HP and the crit wouldn't matter anyway? Heh.