IMO, Sparta was reluctant to start the war, but, once it began, did not want to stop until factors forced them (the captured Spartan prisoners). But I don't think this was more of an agressive Spartan oppinion, but rather the oppinion if their allies. If Sparta agreed to peace, their allies would (and did) refuse to cooperate. Without them following Spartan oppionion, the Peloponnesian League would collaps.
Athens, on the other hand, did experience War Weariness, but this is the kind of stuff you'd expect when your homes were destroyed, and nothing that could be contributed especially towards Democracy. After the Peace of Nicias became what appeared to be a Spartan batrayal, many Athenians felt that they couldn't trust Sparta in every circumstance.
I think, if equal, Low WW is a bad idea, no WW would be fine (although one less strategic decision).