Making decisions about which units to make in imp: question

Say you have a 1 v 1 between 2 civs that both have 2 strong late game army compositions that both counter each other.

One example might be Incas vs Mayans. Are there other examples?

If the Mayans go for eagles the Incas would be at a disadvantage if they also went for eagles, because the Mayan eagles beat incan ones in combat, so the incan player might want to go for slingers or kamayuks instead.

If the Mayan player goes for archers, the incan player does want to go eagles because incan eagles are great against archers, and if they go into slingers anticipating eagles they will be worse off

Can you predict what units your opponent is going for before investing in expensive upgrades? If you make the wrong call, should you switch and get the other upgrades?

Maybe other civs that play like this are Turks vs Italians with gunpowder/cav archers vs condettiero or genoese crossbows