Or at least, I'm not sure that the differences you describe are due to HotD being written better, rather than just because it inherently has a more subtle plot, that's more focused and hence permits more depth in some regards. Though of course that's still a good enough reason for preferring it over GoT, so fair enough there.
I might have to both reread and rewatch to fully assess, but the way I remember it, given the inevitable constraints of adapting such long novels into television seasons, I don't recall many bad calls in what they cut - and I do absolutely think they changed some things for the better. Cersei is the most obvious case - in the books she doesn't get any PoVs until the fourth book iirc, and when she does, it's disappointing as she's depicted as almost cartoonishly self-centered and incompetent, even in her own PoV chapters. GoT Cersei (again, early seasons - haven't even seen the later ones) is definitely an improvement over the book version. You make a distinction between the personal drama that they did well and the politics/worldbuilding they didn't do so well - but in those books, the personal drama and the politics are pretty much the same thing, aren't they? King Robert's murder, Ned Stark's downfall, the Red Wedding, Daenerys' and Viserys' early storyline, they're all politically crucial events that happen because of the personalities of the leaders involved and their petty desires, not because of any great political theory.
And as for worldbuilding, honestly, how much worldbuilding is there in HotD? It's only due to its being a spinoff of GoT that it can expect viewers to get all sorts of things about the setting without being told explicitly. As a prior books fan, it's always hard to judge if the worldbuilding in GoT was sufficient or not, as I didn't need it - but they tried (and their genius title sequence helped).
My favourite thing about HotD is similar to yours it seems - the tragedy and realism of the slow build towards civil war, most particularly the personal relationship between Rhaenyra and Alicent. Loved that big family dinner scene late in the season, where you can still see their lingering affection for each other despite the increasingly cut-throat politics between their respective camps, with Viserys caught in the middle. Though the bit with Alicent misunderstanding Viserys' deathbed comments was pretty lame (or, to quote a meme I saw on the topic, "Be so real, Alicent!"
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But again, I don't think I agree with the juxtaposition - for one, HotD has some of GoT's infamous 'sexposition' too, like the creepy Larys stuff or the even more creepy scenes between teenage Rhaenyra and Daemon. And (though yes, here too it's tough to remember precisely how much was in the show and how much I only know from the books) while Joffrey, the Mountain and a few others are depicted as downright psychopaths without even Aemond's limited redeeming qualities, the motivations of the Lannister leaders Tywin, Jaime and Cersei, or those of the other leading figures make perfect sense, they're just in a different political background. Littlefinger and Varys, fair enough, those are a lot murkier - but honestly, they are in the books too, that's not really the show writers' fault.
GoT is the story of a political free for all due to the downfall of House Targaryen 15-ish years earlier, HotD is the story of an internal civil war within the House in a period in which it still had an iron grip on Westeros, so very different situations in which you naturally see different things - but both shows have some top notch writing and acting, imho.
Yeah, I see what you mean but I figure it's more a matter of the plot the respective shows dealt with, than of a difference in the writers' approach as such. But I suppose we should see more evidence in either direction in the next season of HotD, when they move from slow build-up to open war and big dragon battles... let's see how the shows compare after that.
