Both, for two main groups of reason.
The first one is that when the available positions in society are highly unequal, then equality of opportunity may simply not be enough for a fair outcome, as who ends up in the comfortable and high-status position ends up largely being down to mere luck.
The second one is that (at least as long as families and inheritance are a thing) the two are linked anyway. Inequality of resources and status is the leading cause of inequality of opportunity, after all. You basically have to either go Brave New World or increase equality of resources in generation N in order to make serious progress towards equality of opportunity in generation N+1.
And we agree that a lot of it is about a matter of degree -- I've said as much in my original post, after all :)
Some people are worse than others. Some people are less useful to society than others, though that doesn't make them worse. Some people, given large amounts of money, can do amazing things for the world. On a whim, I can think of Elon Musk. If he weren't allowed to have his fortune from Paypal because inequality is unethical... who would have gotten that money? A government? What would they have done with that money? And why is government/the public always the best decider of how wealth is spent?
Your argument may be reasonable in degrees: Who needs $500 billion dollars? Should there be a legal requirement to invest that money in the public at a certain point, if it isn't taxed directly? I don't know. But I believe inequality is ethical and necessary.