Is there any way to argue that capitalism has upgraded the equalitarian expectations?Compared with socialism: how the removal of personal property, in socialism, levels the ‘playing field.’?
It is difficult to make clear arguments on this point because there are so many shades of capitalism and so many different ways of defining equality and inequality. For example, the United States and Sweden are both capitalist countries, but their mix of capitalism and government intervention is not the same. They also have, according to the GINI index, very different levels of economic inequality. Therefore, it is rather difficult to say that there is one thing called capitalism that affects the level of equalitarianism in various countries.
You can certainly argue that the countries that have the least equality in the world today are the countries that are less capitalistic (understand, though, that we have no data for communist countries like Cuba or North Korea). These are countries like Haiti and Thailand where the economies are much more controlled and are in the hands of "crony capitalists" who use the government to reinforce their power.
You can also argue that capitalism raises overall levels of wealth and that this is fundamentally equalitarian. You can argue that Bill Gates and I are relatively equal because we are both able to easily afford a middle class lifestyle. (He can afford more, of course...) You can say that this is more equality than is seen between a person who is middle class and one who is in poverty, even if the absolute gap in incomes between me and Bill Gates is much greater than the gap between me and a poor person.