bullet construction, as others have touched on, plays a huge role. I think some refer to this as sectional density. They way I think of it is...
imagine you have a rod. If the rod hits a hard target shaped like an "I" then the force behind it is spread over a much larger area and it does not penetrate as well. If it hits same target on it's end... like a "." then this same force is applied over a much smaller area, so penetration is greater.
This is fundamental in that it keeps the variables to a minimum. Say you have the same density projectile and same shape (rod) and the same direction of impact ("." - straight on) but you alter the length of one projectile... well to compensate for the shorter length you have to increase it's size (make it thicker) so now you have a long "." vs a shorter "o"
You can make penetration complicated by adding variables mentioned above like velocity, density, construction, shape, materials... etc. endless possibilities.
What many discussions come down to here is the momentum of a given bullet and it's sectional density. Sectional density is like the "." vs "o" comparison above - the same density object but the "." has a greater sectional density and the force is applied over a smaller surface area of the same target, so it takes a greater length of the same medium (think penetration depth) to slow it down.
At least this is how I make sense of the big issue. I am not aware, however, which matters more and what the relationship is between sectional density and momentum because although it appears that the 230 gr ball would have a greater momentum, the 9mm 147gr frequently has greater penetration. Thus it would appear that SD trumps momentum in this case, although momentum allows for greater knockdown power (relative, think bowling pins).