As I understand it, the best combination of "price and quality" is achieved with a good Warrior, one expert in a suitable element, and with resistance. I don't think such a hero can be called a Battle Mage; in battle, he will only use spells of level 1 or 2. Such a Warrior will almost certainly overwhelm his Mage opponent, all other things being equal.
Of course, there can be exceptions, such as a Berserker, on the Mage's side. But the Warrior can also get lucky with a Sphere of Suppression, or a Cloak of Negation... or even just some artifact that provides antimagic or resistance.
Therefore, my unequivocal, subjective verdict is that the Warrior will win in most battles! :)
If a Warrior can use magic and does so in battle, then he is a Battle Mage!
Sometimes, without magic, even the strongest Warrior cannot pass a test...
I created a small map for testing, but here's the problem: with "correct" defense, the Mage always dies, and only the Battle Mage wins the game. And with incorrect defense, only the Mage wins the game...
Without the Sphere of Suppression, the Warrior sometimes simply cannot survive...
However, in fast-paced gameplay, when Heroes need to develop, the Warrior can become the only Favorite and Winner!
Conclusion: Heroes of Might and Magic III is very well-balanced!
Map for testing:
http://corksink.narod.ru/all/02game/rargame/Test_HW_CORKSINK.rar
