Which works better.....
 

The type of AC and oil cooler screens that attach to the units, or the type that attach to the backside of the front bumper? I am concerned about issues like air flow, debris accumulation, and longevity. If this is answered somewhere else, please direct me there.

The percentage of open area in the mesh is the main consideration. Something above 60% should be used. I doubt if it makes any difference whether the grids are mounted to the coolers or behind the bumper openings.