To be ruled by a superior is not contrary however to human liberty, dignity and equality. Only the despot offends thus . . . even in the state of innocence there would have been political subjection, there would have been a difference of sexes, faculties and power; therefore an order of precedence and subjection. Among the angels there is a hierarchy of order with precedence and succession; why not among men? Therefore it is not contrary to liberty, nor humiliating to the dignity of man to be ruled by his legitimate superiors. . . . There is a difference between political subjection and servile subjection.
-St. Robert Bellarmine, De Laicis
The War for Christendom 
I would say it is in contradiction to equality, just by definition, at least in some regard.
We might notice the difference between ‘political subjection’, or Traditional subjection, and servile subjection, which is the subjugation to raw power, are different in the nature of the ruler’s legitimacy. Jesus directly denounces ‘tyranny’ in the Bible, which was a specific form of government by demotic thuggery in Greece. Instead His proscription of leadership was one of service to the lesser. I would propose that this was the mark of a true monarch.
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In the same chapter of De Laicis, St. Bellarmine qualifies this statement: “when he [Saint Gregory the Great] says, ‘All men are equal by nature, but are made unequal by sin, and therefore one should be ruled over by another,’ he does not mean that men by nature are equal in wisdom or in grace, but equal in essence and in human form, from which equality he rightly infers that one should not be dominated over by another, as man dominates over the beasts, but only that one should be ruled over politically by another.” So in this sense there is an equality of Human Nature which is not contradicted by political rule.
In De Officio Principis, St. Bellarmine summarizes the concept of King as servant: “Kings must not grow insolent or contemn private men; but they should carry their scepter, not in pride, but as a cross.” One immediately thinks of HRE Rudolf, the first Hapsburg King-Emperor, who when the scepter could not be found, took up an actual crucifix in its place at his coronation.
Just a side note, St, Thomas Aquinas was more of the opinion that Tyranny is the corruption of Monarchy, and that just as Monarchy is under certain circumstances the best form of government (indeed, the only supranational government under which other governments flourish), so tyranny is the worst (Corruptio optimi pessima). Even Democracy seeks some (corrupted) form of a Common Good, whereas the Common Good is completely absent from Tyranny. Hence a good Republic is inherently better than a bad Monarchy.
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