All states are different. If your state has a "reciprocity agreement" with GA, then it is my understanding you will pay the AL sales tax. If you pay the GA tax, then AL will credit you or charge you more, depending on the difference. Best thing would be to get a temp tag to drive the car out of GA (since you are not going to register it there, and thus won't pay sales tax there) and then pay the AL sales tax.
But I'm only going by reciprocity agreements in states I"m familiar with, so you'd best contact your AL DMV to confirm this.