Unfortunately I can't offer you any real numbers but I can tell you that it wouldn't be much.
D Alkalines have a capacity of around 12,000 mAh whereas an AA has a capacity of 2,000 mAh. There are other factors involved but the runtime on a 6D mag is already pretty poor (around 2 hours to reach 50% brightness) so I imagine 6AAs would be just that much worse. I'm sure one of the resident experts will come around and give you a more concrete answer.