No, the contact surface in greater on 10 inches vs 3 inches, so there is more friction breaking.
If contact surface were the only variable, this statement would be correct. But it isn't. The force pushing the rope against the surface is the other variable. The actual force squeezing the rope against the surface of the bollard at a given point is a consequence of two variables, the tension of the rope at that point and the radius of curvature at that point. The larger radius in the one case is compensated by proportionately smaller squeeze force. The result is the radius turns out not to matter--only the number of degrees of wrap.
I do not believe this to be true. It runs counter to my experience.
I can't argue with your experience, and I don't have enough experience myself to have an opinion on the matter. But I have a three general observations that might be relevant.
One, the equations governing friction are approximate. They don't have the precision and universality of, say, the law of conservation of momentum. Friction itself is poorly defined. When your rope is rubbing across the rough bark of a limb, and when the jagged surface of the bark is actually picking and grabbing the fibers of the rope (the velcro effect), do we count that as friction or something else? It certainly requires force to overcome, as does friction. The equations governing friction are idealized: they apply to the force required to slide two perfectly smooth surfaces across each other.
But there is no such thing as a smooth surface. At the molecular level, the surface is always rough.
Two, the equations state that the frictional force in a given situation is proportional to the normal force, that is, the force pushing the surfaces together. You can tell right away that this relation can only hold over a limited range of values, and outside that range, it will break down badly. (I can't apply a million tons to one square inch of surface and then measure the friction between the two objects--the objects will be destroyed.) But over a usefully wide range of values the equations hold pretty well, which is why they are printed in physics books and why a Port-a-Wrap works predictably over the range of loads that a person is likely to apply.
Three, the rope is deformed when it wraps around a bollard. Where the rope is under the greatest tension, nearest the moving load, it is flattened the most. This "footprint" of the rope is the area of contact, but the force is not uniform clear across this footprint. The normal force is much greater at the center and drops to zero at the very edge. At the other end of the wrap, nearest the controlling hand, the rope tension is much less, the flattening is less, and the footprint is much narrower, but the force distribution is still non-uniform. I suspect that when you combine the odd force distribution with the fact that both the rope and the wood have rough surfaces (meaning lots of velcro effect), you might expect the equations to break down a bit.
Still, if you did a careful experiment with two smoothly sanded limbs of different diameters, using a modest load of, say, 200 lbs or so, I'll bet you would find the controlling force nearly the same in both cases, close enough to conclude "this is a useful rule of thumb" rather than "this is not true."