The Nazis were liked by many countries and people while the first order were hated throughout the galaxy and the empire helped a lot of worlds

The Galactic Empire has the most obvious correlations but at the same time the GE seems based somewhat on the American government under the Nixon Administration (though more so in the OT as opposed to other sources of Canon). I mean it's obvious. Chancellor becomes a dictator. Army called Stormtroopers. Several members of the Empire are very clearly based on real life members of the Nazi Party. Not to mention the flared hip breeches on the costumes.

The First Order represents the idea of Neo-Nazis. Those who idealise a false version of history and seek to reclaim that alleged glory. Only in this case a much larger and stronger faction of them than appear in real life. Nevertheless the parallels are still here. It double downs on the zealotry and fanaticism of the ideology. A lot of the leadership are young fanatics. The overcoats the FO officers wear are very much inspired by certain regalia.

The Empire is more similar to the Nazis on a functional level, whereas the First Order is more similar to the Nazis on an iconographic level.

The Empire's ways of suppressing dissenting thoughts & behaviour among its own people, oppression & exploitation of those in the Empire who were not members of the elite citizens of the core worlds, & persecution & eradication of species considered unfit to live by Imperial standards, more closely match the nazis. The First Order spent their screen time just trying to conquer the galaxy. If they'd succeeded maybe they would've become more nazi like, but that never actually took place.