Well to put the cat among the pigeons I generally run the left to the front brake as the curve of the brake cable is smoother, it's a straight run and makes the most sense to me....
Me too. All my continental pro heroes did it this way and therefore I did as well.
My winter bike (a CX frame) has the top tube cable routing exactly as stated. It has canti brakes though as befits a CX machine. I wonder why yours has this arrangement and is fitted with side pulls? The left route is the rear brake, centre is rear mech and right is front mech. I just let the cabling from the levers take their most natural course.
Actually - I'm wrong! Centre route is front mech and right hand route is rear mech. Here's a photo to show it and how the handlebar cabling is arranged.