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 endurance and resistance to harm. The fight at the end of MI:2 is a testament to the amount of hurt Hunt can take and still win. Bond is brute force to Hunt’s acrobatics. However, Bourne is all skill. Unlike the others, he is a government Super Soldier. Bourne would likely be on the defensive until a clear victor emerged between the street fight of Hunt and Bond. The victor would probably be Hunt, but still no match for Bourne.
Round 3: The fighters all begin with a modern handgun in an area with plenty of cover and at a suffiecent distance from each other. They are all both hunters and prey. The fact that Bourne managed to get close enough to take out a sniper with a shotgun in the Bourne Identity says something. He kills Hunt right away. Bond has been in this position before in The Man with the Golden Gun. He knows how to be silent and is as good of a shot of Bourne. But Bourne’s battles are often with fellow super soliders from Operation Treadstone, much better training then the spys at SPECTRE. A double O is still only human compared to the heightened reflexes of Bourne. There would be a long quiet to get into position, but it would end with both opponents spoting each other at the same time a one shot from Jason Bourne’s gun. The quickest draw effect.
Results: Bond 1, Bourne 2, Hunt 0. True, the three round format is flawed. In reality, any one of these rounds would result in two kills, but in reality these people don’t exist. It is most likely that the winner of this bloody exchange would be Jason Bourne.
As per usual, feel free to digress in the comments. Everyone is entitled to their opinions.