As DucatiKiller notes, coasting downhill in neutral is usually considered unsafe, as it increases the chances of overheating your brakes. It is also illegal in many jurisdictions.
Questions about driving techniques are generally off topic here, but you do have a question about how engines work that I think is (maybe marginally) appropriate: why do you get better mileage when coasting in gear?
If you coast in neutral, the only source of energy to keep the engine running is burning fuel to idle it. You consume the same amount of fuel as if you were stopped in neutral. (You don't want to turn off the engine completely, as then you will not have power steering, power brakes, air conditioning, or any other accessories.)
However, if you coast in gear, most modern cars have a feature called deceleration fuel cutoff. (If someone knows of a good link about this, please mention it; I had trouble finding one.) When coasting in gear, the wheels supply plenty of energy to keep the engine running, and in turn runs the car's other systems. So the car can, and does, shut off the fuel supply completely, reducing your fuel consumption to zero. (A side benefit of this is that you get better engine braking.)
So in answer to your question: on a modern car, shifting to neutral on a decline is typically less fuel efficient, in addition to being less safe.