^ don't listen to that guy, I use a HawkEye ****** with a Bee ****** and it works great.
Kapowski reply has the answer to the topic question. The secret to using the Hawkie with Zer0 is the Bee. Without the Bee, StormWolf is absolutely right, It sucks big time.
IDK how the fancy mathematics of criticals, amp damages and multipliers of GBX works, but with the Bee, and scoring criticals, the Skookum Hawk Eye in Zer0's hands is outdamaged only by two rifles - the Volcano and the Longbow (and exclusively against flesh-only enemies).
But this two preconditions, criticals + the Bee, leads to a very especific style of playing, more like classic sniping. You shoot the enemy, the enemy doesn't shoot you back. He tries, but you use stealth, cloak (deception), terrain, cover and/or range to avoid being shot. This is not always possible in Borderlands. In the majority of the areas, sooner or later you're gonna have to face open fight. In this case, swap the bee with a defensive shield, and the Hawkie with another weapon. If you wanna stay with a sniper rifle, I suggest my dear Lyuda/White Death.