Come on, don't backpedal, you did.

I'm talking about the essential similarity between historical attempts to unify groups of independent polities

Which cannot be essential, given the essential differences between the polities you consider -- for one, the feudal polities weren't independent. For the other, the example you named (or mis-named -- you first gave the Habsburg Empire, which emerged from personal union rather than a meta position, while you meant something else), the Holy Roman Empire, was not an attempt to unify groups, but to keep together parts of a pre-existing falling-apart empire (the Carolingian one).

The essential similarity is this I think: the centralized political authority answered not to popular consent except in indirect ways, but instead it answered to institutional elites who were insulated from popular opinion.

With that, we get back to another basic problem of your analogy I pointed out in the very first reply: none of the polities in the feudal HRC were democracies. No indirect answering to popular consent. That top-level feudal overlords are undemocratic in an undemocratic feudal world, let's say, doesn't come as a surprise... As for the EU,  by all democratic deficits, you should not forget about the EP, and about referendums.

Or are the differences between them and the present EU in fact so great as to make them useless as case studies?

Since I don't see them as historical predecessors, not direct at least (the EU's structure is in no small part modelled on the federal structure of West Germany, so there the long lineage back to the HRE behind that; but just the strength of the intergovernmental side is a deviation), I would obviously say yes. To be more specific, I can't compare feudal lords with their own kingdoms elected for life to people without other positions elected for fixed terms.

_{*Lunatic*, n.
One whose delusions are out of fashion.}