In general the economic lot of ordinary white workers in America was much better than that of European peasants. The difference in height between first generation and second generation immigrants has long portrayed in graphic terms the better diet of Americans. I have seen estimates that before the French Revolution American wages were twice those in Europe, and I don't think that ratio changed much until after WWI.
As a corollary, I suspect, women had it better on average. The textile mills of Massachusetts and New Hampshire mainly employed farm girls from New England until the Irish Potato Famine brought large numbers of cheaper (male) workers from Europe. One of the complaints at the time was that it was too easy to oppress these immigrants, and the relatively humane conditions of the New England women, who could usually go home to the farm if things got too bad, were replaced by more oppressive conditions. Longer hours (seems crazy given the hours Zinn reports), lower wages, less chance of advancement.
Not just any Americans. Particular groups were able to manipulate the system: contractors ("entrepreneurs"), land speculators and politicians seemed to drive a lot of the process.
What I found most striking was the repeated subterfuge of the use of law. From the time of Roger Williams, early in colonial history, the Americans seemed to have no scruples about making agreements and then breaking them. Some of that parallels the behavior of the Europeans: a treaty was an arrangement for the cessation of hostilities, and a region might easily change hands back and forth 10 times over a century, depending on the way new treaties shook out the military realities. In that context, Americans seemed to seize the advantage given by their greater knowledge of the world. They recognized that the strength on their side was just going to keep growing, so they would benefit by pretending to grant perpetual rights, which they could then take away when their strength had grown some more.
I was pleased to see that there were some objections at the time, though they seemed to come mainly from the Northerners who had fenced in their aboriginal groups long before. The story of the missionaries in Georgia who were imprisoned for objecting to the violation of the treaties gave me some encouragement.
And how about Andrew Jackson refusing to enforce the ruling of the Supreme Court? No wonder Trump admires him.
I'm not sure hierarchy of races had much to do with it. Europeans were used to the rules being made by the ones with the armies. Cleverness meant figuring out who were rising powers and who were declining and lining up with the correct side. In North America that was a fairly easy call.
This kind of overlooks the role of the Radical Republicans in trying to re-make the South, reminding us of US behavior later in the Philippines, Europe after WWI, and Japan and Germany after WWII. The rare bird of idealism shows up with much greater frequency after American wars than European. Granted that opposing the force of commercial interest was generally hopeless, it is still unwise to completely dismiss the force of ideals.
It's true and important that the North was never particularly sympathetic to African-Americans. Lincoln tended to make the argument in terms of economic development (he was a Whig, dedicated to the principle of advancement for common people, by investment and education, and slaves would not get educated). His appeal in the face of Secession was to save the Union (a great struggle to determine "if that nation, or any nation so conceived and so dedicated, could long endure upon the earth.")
I think he probably would have moderated the program of the Radical Republicans, allowing some caste system to be formalized, but maybe not: they had the temporary advantage of no Southern Secessionists in the House or Senate, and it is typical of a party even with such a tenuous hold to use it to pass their program.