Oxford beats Cambridge at politics, as it clearly does, because Oxford is primarily a school of humanities and Cambridge of natural sciences. Politics, like the study of history, is more of an art than a science.
But this won't do. Of our post-war Oxonian PM's, not one actually read history. Attlee and Blair did law - a mere vocational subject which doesn't really count. Thatcher - our most dominant PM - did stinks. Macmillan read classics. Arguably the three most ineffectual PMs of the post-war era (excluding Major and Callaghan who went to the University of Life) all read humanities: Eden (oriental languages), Heath and Wilson (PPE).
Maybe, then, there's another explanation for Oxford's dominance. It's not that the cleverest people go to Oxford. True as this probably is, it's irrelevant because cleverness is neither necessary not sufficient for success in politics.
Instead, Arnold Kling hints at one explanation in this fine essay. Politicians, he says, are selected for their dogmatism: "Anyone with humility seems to be selected against in the world of politics."
This is where an Oxford education prepares one for success in politics. The tutorial system kills humility. It teaches people how to appear to be smarter than they are - which is great preparation for politics. And it fosters in its students an exaggerated confidence in their own ability; after all, if you can match your tutor in intellectual combat for an hour, you must be really clever, mustn't you? It's a small step from here to wanting to share your great ideas with others. Hence Oxonians' dominance in politics. And journalism. (And blogging?)
This, though, is not the only explanation. Here's another one. And for more Oxford snobbery, there's always An Englishman's Castle.