The original Batman and his son, Damian Wayne, are two of the most highly skilled and trained individuals in comics. Both manage to hold their own and usually win against Earthly and otherworldly threats despite not having any powers. The two have butted heads before, usually ending with one giving up so as to not hurt the other too bad, but what if they battled in their primes, without holding back?
The Caped Crusader and his son both have extensive training in combat. Bruce learned from some of the greatest fighters all over the world, mastering dozens of forms of martial arts. Damian received his training from both his father and the deadly League of Assassins. Bruce Wayne is often shown to be in his prime in main continuity. Damian on the other hand is usually shown to be an aggressive but capable fighter. He's arguably at his best physically when he takes up the mantle of Batman in the far future. Created by Grant Morrison and Andy Kubert in Batman #666, this alternate version of Damian Wayne is a much crueler version of the Dark Knight than his father.
Where Bruce values his morals more than anything, Damian's willing to do whatever it takes to protect Gotham, and has no problem with injuring or even killing his enemies. While this alone could prove Damian would beat out his father, it's more of his abilities that put him out on top. In Batman #666, Damian is said to have made a deal with the Devil to gain immortality through a healing factor, even surviving a nuclear bombing of the city. In addition to his powers, Damian also has the benefit of future technology far more advanced than Bruce's. In this future, Damian has booby trapped every prominent building in Gotham and uses Brother Eye as a surveillance system. Bruce has dealt with some pretty unstoppable forces before, but an immortal Batman who isn't afraid to kill, and one who possibly has personal vendettas against him is a pretty tough challenge.
It's certainly true that Bruce has handled supernatural forces before, even inventing some ghost-proof gloves that would allow him to actually punch a ghosts. He is a master strategist who has even devised plans for taking down every single member of the Justice League, but none of them are practically immortal. While it seems like Bruce can defeat anything he plans for, he's never faced anything quite like Damian Wayne's Batman, and wouldn't be prepared enough to take him out. It's likely he'd be able to hold his own, but would ultimately lose out to Damian.With Damian's healing ability, all of Batman's effort would probably result in very little damage. He would likely exhaust every avenue between his martial arts, his gadgets, and his wits, and Damian would still be standing.
These two have fought plenty of people both super-powered and not, but if pitted against each other in a no holds fight they would both face one of their toughest matches. Ultimately, the most likely winner is Damian. He possesses physical skills, abilities, and supernatural powers that are unrivaled in a fight to the death. Bruce would definitely not go down without a fight against Damian, but even the original Batman loses some battles.