Bond has one potential advantage.
Bond fan that I am, I know the winner on paper (or in the BondVerse MI6's incredible data crunching battle simulation super computer) is Bourne. However Bourne doesn't have whats Really kept Bond alive all these years…Dumb Luck!
How often is it the inability of 20 trained soldiers to shoot straight, of a henchman looking left instead of right, of some piece of equipment failing the villain, a random civilian merging into the high speed car chase, of a completely loyal hench or lover suddenly betraying the villian, etc etc that saves Bond?
In this scenario Bond holds up a bit longer than the average counter agent Bourne fights (probably by sucessfully dodging many of Bourne's moves as opposed to overpowering Bourne and by not following a 'typical' series of moves in a given fighting style), but soon hes on the ropes. Bourne is about to deliver the killing move by way of fist, foot, head…paper napkin, whatever. Or hes about to cripple Bond in an attempt to get him to talk. When suddenly the wind picks up and either…
A passing Bread truck ,swerving to avoid something rolling into the street, jumps the curb and as Bourne is now,oddly, incapable of doing more than holding his arms in front of his face is hit by the truck.
A bag of flour flies out the same Bread truck; bursting open it covers and blinds Bourne. A couple poorly executed moves and Bourne is thrown off a convenient bridge/overpass or comically locked in a dumpster.
Whatever it is that defeats Bourne it'll be singularly uninteresting.
It'll be a Porsche Bread Truck with recognizable brand name flour that nearly hits them both. As a crowd starts to gather Bourne takes the truck, Bond steals another name brand luxury car and a chase ensues. Bond forces Bourne into crashing the truck into an internationally recognizable restaurant chain.
Somehow they both windup atop the Bread truck so the fight can go on another 20 minutes as the truck goes thru heavy trafic. Bond hates it as he thinks he's winning but M orders Q to take Bourne out with a miniature drone. Bond winds up sitting stop the truck with the dead or unconcious Bourne next to him.
In all these scenarios the next thing to happen:
M: (via wrist communicator or cel phone) Bond, who is it? Is this the American rogue agent? (Ya know Felix was asked about Bourne earlier in the move and totally lied about him,Treadstone etc ;)
Bond: An American? Yes, Bourne and Bread. (straightens tie, music sting)