Ground rules: Each combatant works alone, no MI6 or IMF lending a hand. Q is out too, no gadgets allowed. The fight is broken down into three rounds: 1st. A car chase; 2nd. Fisticuffs; 3rd. A shootout.
Personal bias: I've watched James Bond movies my whole life and, for my money, Mission Impossible and the Bourne films fall short of Casino Royale. The Bourne Supermacy and Ultimatum are both close seconds. The third Mission Impossible kinda sucked.
Round 1: Bond will opt for a European sports car no doubt, Bourne will pick something more rugged, and Hunt will get a motorcycle...bad choice. The bike won't handle the first collision, leaving the two more experienced drivers. Bond will out maneuver Bourne on every turn, but Bourne can take the punishment and trick Bond into a vulnerable angle T-boning his vehicle. Bond manages to drift away from sure defeat due in part to his uncanny luck and unwillingness to lose. He would challenge Bourne to a daredevil chase up a mountain in which he would dive out of the car before launching it into a blind curve and over the cliff. Bourne follows to certain defeat/death.
Round 2: Each of the fighters have exhibited superhuman ...