If you're looking to increase realism with bows in D&D, you're going to have to increase range penalties. According to the PHB, a melee attack does not represent a single swing of a sword, but rather a series of strikes and parries, with the chance of landing one solid blow.
A heavy crossbow, on the other hand, can fire a single shot up to 120 feet away without a range penalty.
All else being equal, the attack rolls on the two above attacks are the same (both based on BAB, plus ability modifier, which we'll assume is equal). A single crossbow shot fired at someone 120 feet away, versus a series of melee attack against someone 5 feet away, and both have the same probability to hit? That's a problem if you're looking for realism.
For more realism, up the damage on your missiles significantly, and up the range penalties as well (including a penalty for the first range increment).
I'm not saying you should do this, for it alters game balance, but you could do it if you wanted more realism.
In the real world, archers are far more deadly when en masse; they can fire volleys into throngs of opponents, without having to aim at a particular target. How easy is it to hit a single humanoid target 120 feet away? Not very bloody easy, I would say.