If the Monk is not immune to at least Death this would be the most hilariously short battle ever. On the other hand if the Monk is comparable to the Monk from FF XII IZJS, then he would most definitely win. IZJS Monk is ridiculous.

But generally speaking, I'd say they're pretty neatly balanced. The Black Mage can throw out some mass destruction, but the Monk can take it. As soon as it gets to close-quarters-combat the Black Mage loses so it's a matter of if the Monk gets overwhelmed or not. I'd pit my wages on the Black Mage, but it could be a close call.