Actually, being on a hill can be a liability in terms of cover, unless you are behind the crest. When defending a hill top against troops equipped with missile weapons (arrows, javelins, guns, etc.) you always defend the reverse slope of the hill. If you are defending the reverse slope the enemy can only hit you with howitzers, unless he is very close. If you defend the forward slope, your troops expose more of their formation to missile fire, because the men in the front row cannot completely cover the men behind them with their shields (because the rear ranks are higher up then they are). This happened to some of the Roman formations at Carrhae (53 BC). The disadvantage of defending the summit or reverse slope against a shock army is that if you get forced back, the enemy is now pursuing you down the hill. This happened to the Spartan left flank at Sellasia (222 BC). Defending the reverse slope gives you great cover, but it takes away any advantage you have in terms of visibility (because the other side of the hill is dead ground). It also cancels any advantage you get from throwing weapons down the hill.
Of course defending the reverse slope of a hill has some other advantages as well - you can only hit the enemy at very close range. Usually in modern warfare this is a good thing - because it maximizes the effect of your fire power. Not only that, but if the enemy sends tanks at you, they expose their belly armor as they come over the crest of the hill - this is bad news for nearly all tanks. An instance of this is the battle of El Gitar in Tunisia (1943), where the American 2nd Corps repelled an attack by 10th Panzer.
It is never a bad thing to make the enemy climb up to get you. Charging down on them might give you a temporary advantage in shock combat, but it is a big gamble. For one thing, if you do not win at the first rush, then your formation is likely disorganized by the headlong charge down the hill. This is what happened to the Saxon army at Senlac/Hastings (1066). Also, if things don't go well for you, then you have to retreat back up the hill.
So, this is all to say that if you attack down the hill it might be an advantage, but I would not count on it.