I find the claim that wotr is more edgy in its story an interesting one. I feel as though Wrath has the trappings of edginess - demons, gore, etc - but they exist as a natural consequence of the story and events. To me edginess implies revelling in the dark and the gritty and the over the top, drawing attention to it and almost patting itself on the back for putting it in and crucially, edginess kind of ignores the impact of the darkness and gore, which I don't think Wrath ever does. I haven't played any of the evil paths so maybe that happens more in those, but I don't think the game ever glosses over the horror of what happens and in fact, I think it really commits to that horror and tragedy and what it's like on a more human scale, especially in the first two acts, but it still sprinkles that stuff in throughout. And in fairness to BG3, with the exception of durge, I don't think it's as edgy as I expected it to get either. Both games have their moments of it though, to be fair.
On a wider level, overall I think Wrath is the better story and, in my personal opinion, the better game overall but just in terms of story, I think Wrath is more coherent throughout. Its not perfect, but I always understood the motivations of everyone and understood how things broadly tied into each other. Both stories are actually fairly simple at their cores, I think the problem with BG3 is that there's just a lot of... vestigial stuff hanging onto the main plot. Like, the whole githyanki, orpheus plot. Really, there's nothing about the potential githyanki civil war that needs to be part of the main plot. All that matters is that the prism can protect us from becoming thralls. The gith plot doesn't actually inform the main story to any significant degree despite being ostensibly tied to it. The same goes for all the shar stuff. There's so much shar in act 2 specifically, and sharrans stole the prism, but ultimately as far as the main story is concerned, the shar bits function as plot devices and there didn't need to be as much focus put on it as there was. The result is a main plot that's just cluttered, a bunch if individual plots that don't inherently have a reason to connect to the plot.
Meanwhile in Wrath, every quest and plot is thematically tied to the main plot by virtue of it being a war zone that touches every single thing. But more than that, the actual main plot doesn't get cluttered with stuff that is entirely extraneous. It's not a perfect plot, but we don't have factions or sides doing their own thing entirely unconcerned with the main plot.
And just as a parting note here is my obligatory defense for the crusade management. I love it and think it makes the game better to have it in.