Well, if you look at the two city-states critically, Athens would have leaned more toward liberalism while Sparta leaned more toward Conservatism. We’re talking shades of gray here, however.
I could agree with this, but I'd add the fact that Sparta was also by far the more collectivist society while Athens was more individualistic. This underscores how the claim that individualism = rightwing and collectivism = leftwing is nonsense, since you can have both leftwing and rightwing collectivism, or left and rightwing individualism.
Sparta was a totalitarian nightmare--children reared collectively by the State, being left out to die if they weren't physically perfect, and being brutalized into becoming fighting machines. How any conservative (of the American variety) can claim to admire Sparta is absolutely beyond me.