I waited for maddening to play, playing golden deer maddening first playthrough, maybe like 3/4 the way through now. I can't compare to other difficulties, or other houses, or even other classing strategies since I've only played it once, but I can give my thoughts on how it fares as a blind experience first time through.
As for other restrictions I'm also not using any online stuff nor did I recruit characters from other houses. I did get a few of the professors (Catherine, Hanneman, Shamir), but of those I'm really only using Catherine and sticking the others as adjutants. I also am not using divine pulse except for misclicks and stuff like that.
Overall I think it was done very well. Many of the missions really made me think about what I had to do to proceed and try a few different strategies. I hear the enemies have more skills, but it seems class based rather than directly selected like in Fates Conquest. Nonetheless many of them are quite relevant, like pass on the thieves/assassins, and poison strike on the archers.
The big thing is the stats. The enemy stats can be REALLY high. Like falcon knights with almost as much defense as my fortress knights, stuff with so much speed it even doubles my fastest character with the lightest weapon with ignatz' rally boost. Most of my units who aren't really tough just die in one shot to an enemy. It's really crazy, but somehow you can pull off some baller strats and succeed, and finding the way to do it is really interesting. In the early game, and even now, I was pretty much having to use weapon arts on every single attack for both the power and accuracy.
Unfortunately all of the side battles (non-paralogue) are just too easy. I haven't done too many of them because of that, but the ones I've done are just a real downgrade from the main game and paralogues, and TBH I don't really think there's much point to them. It seems like they just kind of put a bunch of dudes on some reused maps and called it a day.
However, the Paralogues were all really cool and interesting. For most of them, doing them as soon as they're available is quite hard. I assume that waiting would help on that, though. Instead of doing so, however, I warp skipped a couple of them, which in the case of the Lorenz one was really fun to figure out how to do. The Catherine / Ashe one was REALLY rough (damn those assassins), but eventually I was able to prevail (though I did delay that one like a month). I didn't get to do the Hilda one, since it said it would be available until May, but then I got timeskipped and it went away, which is a little rude that they lie to you about that. The Marianne one was really fun too, and the Seteth/Flayn one required a very plodding and methodical approach but was pretty interesting to grind out.
As for the main chapters, most of them are really challenging, but some of them are kind of easy, like the burning village (, or the one where all the crest stones are being stolen (I saved about half; it would have been a lot harder to save them all I guess). A lot of the second half of part one was easier than the first half. The lava valley map was kind of easy too, once you know where the allies you have to protect are going to spawn. This is all offset by some REALLY hard maps, like the first two after the timeskip, most of the early ones up to the Tower of Black Winds, the Battle of Eagle and Lion.
Ultimately, I think what's going on is as the game progresses you have a lot more options that mess with the positioning and distance, like warp, rescue, draw back, dancing. And also your units get access to a lot more range. The Thyrsus for example is REALLY strong (sometimes I think it's a bit overpowered, but then some really hard chapters slam me anyway, so IDK). And having these abilities lets you deal with things a lot more effectively.
So the difficulty is ultimately pretty widely varied and inconsistent, but there haven't really been any main chapters and/or paralogues which were trivial, where I didn't have to think hard about how to proceed (except maybe the burning village chapter), and all of the chapters have been very fun to play so overall I am really liking it so far.
As for new 3H mechanics in general, the Battalions are kind of cool, in that I like the passive buffs they give your units, and picking which battalion to assign to which unit is interesting. The gambits are unfortunately pretty lackluster, however; they usually don't really do more damage than normal attacks, and the enemy not counterattacking is less of a big deal than you'd think since many of your units can attack from 3-4 range anyway. Also they're usually a really bad option since they're so inaccurate. Almost always, if I'm attacking an enemy, that enemy needs to go down RIGHT NOW, and betting on some 30-40% gambit ain't gonna cut it. Plus there's quite a lot of skills that involve the battalions, but most of them aren't really good, especially when compared to the skills that buff your stats or weapon skill. Like all these things add strength to gambits, and I don't want the gambits to be stronger, i want them to be more accurate. Or the ability only works when the battalion is at low health which is difficult to deliberately engineer. But the enemy knowing gambits is really interesting, because they don't really have to care about consistency as much, because even a 50% chance of ruining your day is pretty bad. So I guess the gambits are a case of something that is better in the enemy's hands than yours, but I can get behind that. They are pretty effective (since they're accurate) against monsters too, so hey.
The main thing that's interesting about this game compared to other FE games is how it kind of forces you to focus on being really proactive. A lot of the really hard strategizing and planning goes into finding ways to kill things before they get a chance to attack you. Most of the heavy lifting is done on player phase, using everything at your disposal to try to smoke all the enemies that might attack you next turn, because if you let them, they will freaking MURDER you. This is unlike a lot of other FE games, a lot of which is about positioning yourself so that the enemies run into you in an optimal way and kill themselves on your counterattacks. In this way it's a bit like Gaiden, which had a bit of a similar focus, with a lot of far-ranging attacks and fewer but stronger enemies.