According to my experiences, slingers are the most effective missile units in the game, though they are extremely cheap (300-600 Mnarii and easily recruitable (you just need a simple drillground in a ridiculously small village). They are effective against armor, which means they can easily destroy and weaken legionaries, phalanxes and elite units.
Militia don't even stand a chance against them (once the enemy attacked one of my settlements with an army of 1200, mostly levies, I had about 2-3 squads of slingers and some militia units, the slingers have killed about 600-700, which was more than the half of the enemy's army)

However, from my experience, archers are only good against cheap and poorly equipped units, they are completely useless against heavy, elite and armored units. Still, they are lot more expensive than slingers (600-1600 Mnai(!)) and you need large settlements and costly barracks to produce them. (One of my best memories is when 5 units of Syrian Archers were shooting at 1 unit of Pezhetarioi (hellenic phalanx) and they were only able to kill 4 or 6 of them )

So, as I see:
Slingers:
- Extremely cheap
- Easily recruitable
- Effective against armor/heavy/elite units
- Highly mobile

Archers:
- Relatively cheap
- Highly mobile
- Useless against armor/heavy/elite units

What do you think?
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