Its kinda a mind game, this "thinking" that we do. I know you want to know the answer, that's all, but it may not be as simple as all that.
Wood and aluminum and carbon are different critters. There is the ultimate answer, which is better at penetrating, yes, but there is the alternate answer that we shouldn't lose sight of, that all three of them are fine (and have been proven such).
The finish and thickness of the shaft matters a lot, the substrate being penetrated matters a lot, the broadhead type matters a lot, the arrow flight at the time of the hit matters a lot, the weight of the projectile (and even the profile of that weight distribution) matters a lot, the game type ( large or small) matters a lot, the distance of the shot (and ultimate loss of initial speed and momentum) matters a lot, the fact that the critter can move at the wrong second, or simply be pushed by the projectile ( and thus move) can matter a lot.
All of these things can affect the penetration of any given projectile as much or more than the actual make up of the arrow.
My head hurts
ChuckC