Let's remember that Jackson was a military man. Lincoln served in the the Illinois Militia during the Black Hawk war, but never saw combat. Jackson served with a South Carolina regiment as a courier during the Revolution and would become a colonel in the Tennessee Militia in 1801. During the War of 1812 he'd become a Major General fighting in the Creek War portion of the War of 1812. He'd also earn the nickname Old Hickory because he was described as being "tough as old hickory." He'd also become a national hero leading American troops to victory at the Battle of New Orleans. General Jackson would also lead a successful invasion of Florida during the First Seminole War (1817-1819).
Plus Jackson is known to have fought several duels, in at least one of them he killed a man. Lincoln is only known to have been involved in one duel, which was never fought. He managed to get out of the duel by being the one challenged. Dueling etiquette stated that the individual challenged got to select the weapons, and Lincoln selected broadswords over pistols as he knew full well he would have an advantage in height and reach. An advantage that wasn't lost on his challenger, James Shields who agreed to call off the duel.
So if they were to fight who would win? We have a man who had fought in combat and fought and won duels vs. a man who never seen combat and who's only duel was never fought. Even with both in their prime Lincoln's single greatest advantage could have been overcome by Jackson, where as Lincoln could not have over come Jackson's single greatest advantage.