Someone did some heavy mathematics on what weapon to use at different points of the game. He concluded with this:
0. Always pick Highest DPS weapon
1. extra crit damage >100%, crit chance < 35%, use Hxbow, otherwise use bow
2. extra crit damage <100%, crit chance > 35%, use Xbow, otherwise use bow
3. at very beginning and high end with super gear, bow is the best choice
So if your critical damage is over 100% but your crit chance is less than 35%, the hand crossbow is best to use.
If your crit damage is less than 100% but your crit chance is over 35%, the 2-handed crossbow is your best bet.
Early in the game and late in the game (when your fully geared up), the bow is the best.
Its pretty interesting to see that the regular bow will eventually be the best weapon in the game. Although this is true, it is important to pay attention to point 0 (Always pick the highest DPS weapon). So essentially, in end game, if your bow, crossbow, and hand-crossbow are all equal DPS, you should go with the bow, but if any of the weapons do higher damage, then you should use the highest DPS weapon.