User blog comment:Hyperborean/"The House of Hades" – official expectations blog/@comment-99.56.37.183-20130220000819/@comment-3146930-20130220010554

Also, the Argo II is armed with ballista and other weapons so the Greeks do use them, but using ballista during something like Capture the Flag would be incredibly dangerous and they wouldn't really have a reason to use them outside of serious battle. They also mention in The Battle of the Labyrinth that they do use things like catapults, as shown right before the Titan army comes out.

You also have to think that demigods would be more deadly with old fashioned weapons because of who their godly parents are. Apollo for example is the god of archery, not the god of AK-47's. Percy is skilled with Riptide because it draws on the power of the ocean (or something like that). In The Lost Hero, Annabeth offered Piper a gun as her weapon, which she refused in favor of a knife.

Also as stated above, the Romans use old fashioned weapons as well. Not to mention that in The Mark of Athena, it is pointed out by Leo that there were some things the Greeks were better at than the Romans. The Romans for example could never make a working automaton and didn't know how to work Archimedes' Spheres, even if they had made advances in other areas, like aqueducts, roads systems, and public sanitation. They were just better at different stuff.