Black Mages can be one of the most powerful jobs early on if raised right and have the right equipment. One combination players can try is equipping a Black Robe and having the S-Ability Turbo MP from the White Mage. Another idea would be to use the Magic Pow+ ability from the Alchemist. Different elemental rods will enhance the power of the spell (i.e. Flame Rod enhances Firaga).
Hume Black Mages are less powerful but slightly faster than nu mou Black Mages. While most of their stats are mediocre compared to other hume jobs, they have high MP, exceptional Magic Power, and the highest Resistance of all hume jobs.
The moogle race is handicapped when it comes to magic users. Everything the moogle Black Mage can do, either the hume or nu mou Black Mage can do better. This also extends to the moogle's advanced magic job, the Time Mage, which is overshadowed in every stat except defense by the nu mou Time Mage.
The nu mou Black Mage is superior to both the hume and moogle Black Mages in every way that objectively matters. The difference in HP, Speed, and Attack between the three are marginal at best, and there is a substantial increase in MP, Magic Attack, and Resistance, making nu mou Black Mages the most powerful of the three. Nu mou Black Mages have the highest Resistance, tied with moogle Gadgeteers.