ok- your axmen are the same as my dancing sword girls, and your crossbowmen are my archers.
I base my team on the composition of my enemy's team. I look at how many opposing units there are, what the defense bonuses are of each, and plan accordingly. If most of my opponents have bonus defense against incoming arrows, in go the dancing sword chicks. If they're best defended against brute strength, then I send more archers. Then I turn it over to the autofight and hope for the best. Generally speaking, I've found that fewer units in the opposing army are better, even if there are large numbers of them in each unit, than multiple units that are smaller in size.
If I am massively overpowered in numbers, I tuck tail and negotiate.