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I'm playing through the Alliance campaign. After the mage-necromancer Anastasia, the warrior Anton seemed a bit weak at first. Initially. The constant lack of mana and the absence of spells like "Stop" and "Petrify" made battles very difficult and costly. Of course, mages don't have access to physical skills of level 3, but they do have the main ones at levels 1 and 2! (Reinforcements, Battle March, Ambush, War Cry), and their effect is acceptable, both for mages and warriors – for example, maximum damage is maximum for everyone. But without mana, you can't even use them.
The main advantage of a warrior is strengthening their army with physical defense and attack power; it's not very useful to fight hand-to-hand. But what if you're given a small number of troops, who should you strengthen?
A mage will also prefer to strengthen their army or weaken enemies, but they have an advantage over the warrior in this regard – an abundance of mana and magical power.
A warrior with a huge army is a different story. In this case, they are stronger than a mage, who still needs to cast spells to strengthen or weaken, while the warrior's hero's power stats (attack, defense) immediately strengthen the army from the start of the battle.
I think a mage is stronger than a warrior, simply because I play as a mage more often. It's easier to start with them. It's easier to restore fallen units and "disable" enemy units for a while.
A warrior is stronger than a mage when they have a large army. Their units initially deal more damage than the mage's units. Sometimes, the mage simply doesn't have time to restore and strengthen their own units and weaken the enemy units.
Although, everything is so individual, as individual as each player, within the possibilities of Heroes 6