Right now 2H weapons are al but impossible to deal with in captain mode at least, which is 90% of what I've played and everything I say next is also in regards to that.
Nothing other than another 2-hander can lock in melee with 2-handers and win. So excluding,2H vs 2H and given that it's wrong that you can't tell your archers to aim at a specific unit, although understandable to some extent, shields can tank any archers and close the gap, while 2H stay behind them no even scratched.
On the matter of 2H vs shields, units with 2H,are faster, have longer reach,and their swing speed comparable enough for it to make little difference to the AI, and armour plays little role in general, even more so from a swing from a 2H. Units with shields should be able to use their weapon,without exposing their whole body by moving their shield to the side, in order for the attack animation to play. It takes away so much from the usefulness of the shield, resorting to some retarded swinging and movement patterns. Using the shield, while attack would solve the main issue with the shield units acting as either a pin cushion or a roadblock. If 2H manage to flank them, it's game over,but if the shields are anchored to some good terrain and can hold their shieldwall facing the enemy they should at least hold. If (even some) 2H can smash the shields, then the 2H should be made destructible too. You cannot swing a menavlion or a glaive against or while riding a horse at full gallop and expect to be left standing afterwards, or the 2H weapon whole, in either scenario. Lances usually broke after the first charge, and that was while the counter force was along the axis of the lance. Anything with a similar lenght that makes contact at high speeds should break, except for the lances, as that would leave shock cav completely out of options. Also, 2H should break if you keep blocking with them. 10-20 hits from a sword and 1-2 from head of a great axe, should break the handle.
And since I'm on the topic of balancing, armour should be much more effective against arrows. Heavy cav in particularlar suffers from not being able to charge and completely destroy a units of archers,unless it does some bona fine manouvering.
I don't mind getting recked if the something that is recking me would realistically indeed reck me, but archers i.e. not shooting 5 degrees higher to kill the naked barbarians that are the much more serious threat, is not right.