For PVE...
I would suggest going with a crossbow.
Due to its faster firing rate, it has a higher sustained DPS, based on Juju's test.
This makes it a better choice for big HP opponents, like Kartia bosses, raid bosses, etc...
For PVP...
Go with the bow.
It has higher damage per hit, making it a better burst damage weapon.
Also, does higher damage with attack skills.