Athens education system mostly focused on reading writing and public speaking which is crucial to the adult life in Athens. Sparta focuses on training for war every day. Athens education system is better than Sparta's military system because to run a successful city-state you need educated people to run it and if you are always focusing on only making your military better, than your society will be very lacking in the education department. But don't forget that at military camps in Sparta they taught the boys how to read and write, and in Athens at the age of 18, they were sent of to military camps. Athens also did not fall behind in the military department either. In Athens they were way ahead in the naval forces.
I hope that was enough!
