Are you talking about relative (ordinal) inequality, i.e.
who is above whom" on the social strata? Or absolute (cardinal) inequality, i.e. how much more* do people above you have compared to you?
I would argue that the former is self-evidently equal across systems. By definition, if you're speaking in relative terms, for you to rise up the social strata someone else must fall.
I would not argue that this is true in absolute terms - measured in your country's currency, it seems empirically true that certain systems (in particular free-market corporate capitalism) lead to much wider disparities in wealth than others (say, communism). However, I'd argue that if you actually care about absolute wealth rather than relative wealth, this shouldn't matter to you, because the median person in corporate capitalism does far better than even the wealthy in communist countries (we discovered this in the early 90s).
There may be hybridized systems that can still generate adequate absolute wealth while capping relative disparities. I'm skeptical of many of the examples that are often cited, though. IMHO unionized capitalism actively failed during the 70s; people like to blame Reagan or Wall Street for the dismantling of unions & pension plans, but the competitive reality is that the companies that made up this system all went bankrupt because of foreign competition, not because of any particular policies. That's a failure to generate adequate absolute wealth; you can't ignore the existence of outsiders who follow a different system when judging the sustainability of your own system. European-style socialism is intriguing to me, but may suffer from a similar problem: it's unclear to me whether the EU can a.) hold together and b.) avoid getting conquered militarily by outside powers in the absence of the NATO security umbrella.