Liberals loathe the political Right’s hypocrisy and unfairness. Conservatives loathe the Left’s immorality and weakness. The groups’ estimations of their own qualities, though, are less precise.
The question of “hypocrisy” is particularly interesting. La Rochefoucauld noted that “hypocrisy is the respect vice pays to virtue.” One can’t be a hypocrite without recognizing that virtue – that morality – exists. This recognition it itself makes hypocrites superior (in their minds) even to decent, noble liberals who discount “morality” as dogmatic and unrealistic. Think of fundamentalist Christians who think that belief in Jesus is the sole criterion to enter heaven; one’s behaviour is beside the point. So, to the Right hypocrisy is a good thing, though they don’t say so.