Peter H. Lindert, Jeffrey G. Williamson released a NBER paper on just this topic a couple of years ago.
Building what we call social tables, this paper quantifies the level and inequality of American incomes from 1774 to 1860. In 1774 the American colonies had average incomes exceeding those of the Mother Country, even when slave households are included in the aggregate. Between 1774 and 1790, this income advantage over Britain was lost, due to the severe dislocation caused by the fight for Independence. Then between 1790 and 1860 US income per capita grew even faster than previous scholars have estimated. We also find that the South was initially much richer than the North on the eve of Revolution, but then suffered a severe reversal of fortune, so that by 1840 its white population was already poorer than free Northerners. In terms of inequality, our estimates suggest that American colonists had much more equal incomes than did households in England and Wales around 1774. Indeed, New England and the Middle Colonies appear to have been more egalitarian than anywhere else in the measureable world. Income inequality rose dramatically between 1774 and 1860, especially in the South.
In other words, their conclusion is that per capita incomes were higher in the US than pretty much anywhere else in the world at the time, implying lower inequality, even when including slaves in the account.
As for how 1860 inequality compares to today, they've made their complete data series available online. There you can find an XLS chart titled "American Income Inequality 1860." For "all households" (which includes slaves) they find:
| Region | Gini coeff. | Top 1% | Top 5% | Top 10% | Top 20% | 40% | Bottom 40% | Mean | Median |
|---|---|---|---|---|---|---|---|---|---|
| All USA | 0.511 | 10.0 | 25.6 | 38.0 | 54.9 | 34.5 | 10.7 | 829 | 523 |
SO the Gini coefficient in 1860 including slaves they calculate at 0.511. In 2013, the US Gini coefficient was 0.42, but there's a wrinkle in that that number is post tax and transfer. There were far lower taxes and fewer welfare state-type transfers in 1860.
Pre-tax, the US Gini coefficient is 0.57, or slightly above the level of inequality in 1860. That is what US inequality would look like in the absence of transfer programs like Social Security and Medicare.
Counting "free households only," Lindert and Williamson find that the Gini somewhat lower at 0.474. It might seem surprising, but slavery seems to have accounted for less income inequality than Social Security and Medicare do today.
TL;DR - This study finds that income inequality was nearly a full point lower (0.091) in 2013 in the US than it was in 1860 including slaves, or about .05 lower including only free households. However without modern social welfare programs, income inequality in the US today would be substantially higher than in 1860.