You are right, there is a difference between them, especially at the beginning. However, it is not necessarily true that a mage will be stronger than a warrior; he will already have stronger archers than the mage, but without casting any buffs on them, and he will still have a turn left for some kind of speed boost. By the way, it would be interesting to know which levels you consider to be the starting ones, so that I can better understand your opinion.

Levels of what? If it's the levels of units, then the starting ones are the first three or four. If it's the levels of development, then in terms of time, it's the first, second, third, or fourth week, depending on the difficulty, or until all the dwellings are built (even if they are not upgraded).
And in any case, in the first or second week, a mage hero (a combat mage) who has a spellbook with spells and enough mana and strength to use them will defeat a warrior hero who has none of these things. This is assuming equal development.

It is only possible to talk about who is stronger in an abstract way. For example, I get so caught up in the Gameplay that I don't have time to think about who to play as. Moreover, the process of developing a character (which skills to choose, what to buy first - a spellbook or a ballista, etc.) is already well-established. :)

Added 5 minutes later

I can't agree. Just imagine - it's the end of the game, and a decisive battle is taking place between a mage and a warrior, or even better, a mage-warrior and a mage (it doesn't really matter). The mage, of course, relies on magic, and the warrior relies on stats (and let's also assume that the armies are roughly equal). So...
But what if the warrior has an artifact like the Sphere of Inhibition? And what then? And vice versa - if he doesn't have it, then the mage will crush the warrior.

This is a choice that you make throughout the game.

And if we take into account that we are fighting different monsters, then EVERYONE uses both, and the most clever thing is, of course, to combine them, because you need to be ready for anything.

As I said before, all of this is abstract. When we discuss this, I think we are taking heroes, maps, and creatures as a "blank slate," assuming that there are no artifacts, and if there are, they only equalize the forces, and the strengths of the units themselves are equal or compensate for each other.
In addition (regarding the use of both), I try to make sure that all my stats (knowledge, attack, etc.) are off the charts, it doesn't matter which is more, which is less - there will be more attack, more defense, I will attack more, there will be more magic - I will cast more. But, in principle, it is all used harmoniously.