I tend to think of liberty and equality of opportunity as growing side by side and supporting each other, because IMO that's how it's worked in America, at least most of the time. So I get a bit puzzled sometimes as I study early 19th century France and Britain. France was, at least by the standards of the time, admirably egalitarian. You see many cases of men born into poverty and obscurity who rise to prestige on their own merits. But they were ruled by a control freak censor of a dictator. Britain, OTOH, was a highly stratified society largely ruled by a hereditary aristocracy--but was in almost all ways more free and open.
I'm usually pretty good at putting on the mentality of the past, but I guess as a 21st century American I have trouble understanding why the French didn't seize their freedom and the British their equality, because I'd find life without either equally unbearable. (Not, of course, that I'm claiming 2007 America is a perfectly free and equal society. But you don't want me to go into a political rant. Really, you don't.)