I understand that the best combination of "price and quality" is achieved with a good warrior, one expert, and resistance to a suitable element. I don't think such a hero can be called a battle mage; in battle, he will only use 1-2 levels of spells. 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, for example, on the mage's side. But the warrior can also get lucky with a sphere of prohibition, for example, or a cloak of defiance... Or even just with some artifact that provides antimagic or resistance.
Therefore, my unequivocal, subjective verdict is that the warrior will win in most battles! :)