Does the gun have a lower DPS value than the crossbow?
He mentions in the OP that both DPS and damage are higher on the gun.
If the guns stats (i.e. Item level, damage, dps, agility and so on) is higher than your previous weapon and you are doing less damage then before you are doing something wrong. Bows/Guns/Crossbows are all just ranged weapons and only the raical bonus will make a difference.
Unless it has different secondary stats or the testing situations were different, I agree, though I'm not sure how much of a factor weapon speed might play.
To elaborate on the different testing situations: OP, what were you doing when you last recorded the bow damage and when you recorded the gun damage. Seemingly small differences(such as running a PuG versus running the same exact dungeon in a guild group) can make a difference(in the PuG you would have the LFG buff). Or perhaps you're used to running with a particular class that wasn't in the groups that wasn't in your group this time. Or perhaps you leveled and thus you find your crit/hit/haste ratings no longer give you as much bonus per rating.
Short of testing under controlled conditions(same level, same group, same boss, for instance), outside factors can play more than a big enough role to horribly skew your results.