Are you playing as an archer?
Due to archers gaining bonuses to hit and damage, nothing beats raw APR. Tuigan may only have a rather pathetic +1 to damage, but the extra APR is extremely meaningful when you consider the magnitude of the Archer bonuses and weapon proficiency.
From your list, I would rule out the Elven Court Bow, since there is no bonus to damage or APR, and an Archer will have a bitchin THAC0 anyway. I would use Strongarm+2 at the early stages of the game (only bow that has +3 damage), and as your kit bonuses increase, consider switching to Tuigan. I've never been a crossbow fan, due to the inferior APR rate over bows, but they do pack a heavy punch. The ultimate Crossbow will obviously be Firetooth +5, but in the meantime, FIretooth +4 and the Giant Hair Crossbow +3 will both server you well. For maximum damage per round however, use Tuigan or Strongarm depending of your level.
If you are a fighter rather than an Archer, then your average damage per hit is (assuming grandmastery):
- Giant Hair Cross Bow = 14.5
- Firetooth +4/+5 = 15.5/16.5
- Tuigan+1 = 9.5
- Strongarm +2 = 11.5
So it is apparent that the Crossbows win the damage per hit award, but when taking into consideration the fact that bows grant an additional +1 APR base: (the following assume post level 13 and again, grandmastery)
- Giant Hair Cross Bow = 3.5*14.5 = 50.75
- Firetooth +4/+5 = 3.5*15.5=54.25/3.5*16.5=57.75
- Tuigan+1 = 5*9.5 = 47.5
- Strongarm +2 = 4.5*11.5 = 51.75
So, without the bonuses from the archer kit, in terms of damage per round, Strongarm beats Giant Hair and Tuigan, but Firetooth takes the crown.