I would pay it off. Odds are you could sell it for more than the difference of Att next payoff and paying off phone fully.
Another option is seeing how much Apple will repair it/replace it for. I had a hairline crack by the headphone jack that the genius bar said was due to faulty phone production. They swapped it out and my att next plan updated to that phone.
Im an employee for AT&T. If you take it to the store, your trade-in will be denied. One of the questions we have to answer for the trade in is if there is any cracks in the LCD/LED screen. In your case, we would have to answer yes and the trade will be denied.