The existing answer is incorrect. It has incorrect calculations (80 x 1.5 is 120 not 140), and you don't need your opponent to be asleep for Night Shade to work. It's basically the same thing as Seismic Toss except it's Ghost type. It also confuses base power with set damage, Shadow Ball can't have higher base power than Night Shade when Night Shade doesn't have a base power to begin with. So before I answer, I'll explain what this is.
- Set damage moves are moves that have no base power, and instead do a set amount of damage. Night Shade is a set damage move, as it always deals a certain amount of damage, ignoring any extra modifiers like STAB. So yes, Night Shade is like Dragon Rage in this way.
- Base power (like Shadow Ball's base power of 80) is not the amount of damage the move does. It's the number that represents "base" in the damage formula here. So Shadow Ball doesn't always deal 80 damage because of all the extra things considered in the formula, like your Pokemon's attacking stat and your opponent's defending stat.
So to answer the question, no, Shadow Ball is better than Night Shade in most situations. This is because Night Shade deals a weak amount of damage, at least for a competitive battle. 100 HP damage will 3HKO, 4HKO or 5HKO almost every Pokemon in competitive battles, as just about everything has over 200 HP. Shadow Ball, on the other hand, is capable of much more. Backed by a good enough Special Attack stat, it can OHKO Pokemon.
We'll assume you're playing in competitive battles. For this example, imagine that you have a Gengar and you're facing a Medicham. In this situation, you have Night Shade and not Shadow Ball. You use Night Shade. Medicham will take the hit easily, and will be able to take two more Night Shade attacks assuming that it's using the standard EV spread. Medicham uses Zen Headbutt, which will KO Gengar:
>252 Atk Pure Power Medicham Zen Headbutt vs. 0 HP / 0 Def Gengar: 482-570 (184.6 - 218.3%) -- guaranteed OHKO
We'll take the exact same situation again, and this time Gengar has Shadow Ball. Gengar uses Shadow Ball on the Medicham. This is what will happen:
>252+ SpA Gengar Shadow Ball vs. 0 HP / 0 SpD Medicham: 366-432 (140.2 - 165.5%) -- guaranteed OHKO
Notice how it does 366-432 damage instead of just 100? This is why set damage moves are not favourable on most Pokemon, as their normal moves are going to deal more damage in general. The only time where set damage moves are useful is when a Pokemon's attacking stats are so bad that the set damage move will deal more damage. One example is Chansey, who has horrible attacking stats. It uses Seismic Toss (another set damage move) to be able to deal some damage.
Damage calculator used in the examples