Confusingly; it's rather an apples-to-oranges comparison.

For one thing, the HRE existed over a period of nearly a thousand years, and underwent several structural changes in that period; the HRE of one century and the HRE of another could be very different entities to compare to the EU.

For another thing, the HRE was feudal in nature, which introduces all sorts of obligations and forces between the members that don't exist in the EU.

What sort of things were you looking to compare? Economic policy, or Military policy, or Foreign policy? Maybe how members engaged in international diplomacy, and what role the HRE/EU would take in such arrangements?