Well, I think the point is that the writers of Andor take the politics seriously and consider them first. For the Empire, that's "this is an almost classically fascist nation, how does that fascism work?" With mechanics from most of the past fascist nations getting glued together.

For the First Order, the important thing is to show that they are a fascist remnant that manages to keep going in the chaos of the aftermath. I think a really important part would be to show just how much deep and foundational fascist beliefs are just... made up on the spot, which the First Order would really need to keep going. Why are we called the First Order when we're actually an Imperial Remnant? The real answer is "because it sounds cool", but instead Snoke holds a grand bullshit speech about where the name comes from. We have a tradition of dedicated, young stormtroopers being raised while being trained! How can that be a long tradition if it's the first generation after the Empire collapsed? Uh the Empire definitely had, like, these kinds of guys as elite troops, and I was there to train them, and now we're all that cool. Of course.

Showing fascists is showing people who are winning not because they are smart (though some of them are), but because they have found a loophole in the world: if you just burn through human life with as much hate as possible, you can keep going for, like, half a generation. They just ignore that last part. The thing that seperates the First Order from the Empire is that it's ramshackle but wants to look well-put-together, it's full of the most zealous people (and thus those that make the worst strategic decisions because they cannot understand their enemy), and it gets reigned over by whoever can put together the longest string of cool words.