As far as I understand combat mechanics, a skilled soldier with basic equipment will be better than a green recruit with masterwork armor and weapons. A recruit will be hit quite often and some of those hits are going to do damage eventually, even with the best possible armor. A legendary dodger and shield user, on the other hand, will be able to avoid almost every attack and very basic armor will deflect most of the rest.
But: A recruit with decent armor and weapons can cut up a naked and unarmed champion. A soldier does need some kind of weapon to be useful, because unarmed soldiers will just punch (and bruise) an enemy eternally without ever doing serious damage. They can bring someone to the ground, but the probability of killing someone that way is almost zero. In a recent fort, I had 10 soldiers punching an unconscious giant for weeks. One good hit with an axe would have killed it, but they just turned his face into pulp and I had to wait for some caravan guards for the final blow.
Leather armor is useless because even copper weapons will ignore it almost all the time. Copper beats leather, bronze beats copper, iron beats bronze, steel beats iron and adamantine beats steel. Since no (unmodded) enemy has anything better than iron weapons, iron armor works well enough and steel or adamantine gives you near invincibility as long as you have a full set for everybody. If your soldiers have steel (or adamantine) cutting or stabbing weapons, enemy armor is ignored almost completely, but if a recruit isn't skilled enough to hit the enemy, even the best weapons won't help.
/tldr: I the hands of a veteran, any equipment can be deadly; Equipment without skill isn't very useful.