This is a long standing debate between a friend and I

It would be Batman, hands down. He's an olympic level athlete when it comes to Strength, endurance, speed, etc. He's smarter than Indiana Jones in every aspect save for Archeology(and he still knows a lot about such). He's got more tools readily available than Indiana Jones. And let us not forget that Batman is a master of every known martial arts in the world and has an extreme amount of experience in using all of them. Indiana Jones may be able to take a hit pretty well and is an acomplished brawler/boxer, but he hasn't the skill or speed to keep up with Batman. I love Indiana Jones as much as the next fan, but speaking purely on statistics wise, in the end, he might get a lick or two in, but Batman would end up mopping the floor with Dr. Jones.

Batman has come up against some very tough supervillians. So because of his training and his experience in the field, I would surely have to say Batman would win that fight.