What are the main differences and similarities between the marxist and elitist theories on the distribution of power in Liberal democracies?
Elite theory is a scientific theory from the social sciences. It's most strongly associated with sociology, but has touched political science, economics, and probably other bodies of work as well. Elite theory just says that power is concentrated in the hands of a small number of people in society. So if you want to understand the movements of society, you should focus on them.
So the idea of a "distribution of power" here is that power is concentrated in the hands of some small group of people. Elite theory in general does not posit who exactly those elites are, though individual scholars sometimes do. For example Mills (The Power Elite) identifies key military, economic, and political groups that dominate American society.
Marxism is in some sense, far more specific. It's fair to say that while Marxism and Elite Theory are different bodies of work, they do overlap on some key points.
For Marx, all of society is driven by its economy. Capitalist countries all share certain characteristics and follow the same over-all trajectory merely because they are capitalist. In these countries, an elite strata of society called the bourgeoisie control society. They do this by owning the means of production (things like factories, arable land, valuable equipment, etc.). Since they control production, they are able to control all of society.
For a primary source, the Communist Manifesto outlines this in a pretty straight-forward way.
1I would say that Marxism also emphasizes the concept of the group or collective and discourages the concept of the individual.– David SDec 11, 2018 at 17:02
@DavidS I would disagree, but that's outside the scope of the question. This isn't a question about individualism or collectivism. Dec 11, 2018 at 17:49
Your answer covers most of what I would have to to say, though I would argue for inclusion of collectivism as a core component. However, you disagree, so I would have to provide a competing answer. Rather, I'll +1 yours, not enough of a quibble for me.– David SDec 11, 2018 at 21:12