It actually saddens me to see so much hate for Conquest.
Out of the three games in Fates, I actually found it the best.
In Birthright, the entire story is "Anime" to an extreme. It's all super happy, sappy stuff, with a lot of back and forth filler side maps that really didn't need to exist. The story body count is actually higher too. You have people intentionally killing themselves over the dumbest of reasons, and it all felt very out of place. There was no real character development to be had here. Everyone pretty much stays the same. (Start with this game first if you want the worst experience first)
Conquest, for me, had a better written staff. They were more interesting, felt more like an actual fire emblem game, and had a progressing plot that just felt more natural to the story. I'll have to watch Aki's "Two faces of Xander" character later, but Xander was actually my favorite character in the game, and I felt he gets unfairly shit on a lot, without really looking at his character in an unbiased way. Everyone else actually gets quite a bit of character development, and you can see where they are all coming from.
In either storyline, the opposite faction is written in such a way that they are intentionally designed to look stupid, and very concrete in their beliefs that the hero was stolen from them, and all hell will pay, and the only way to sate it is with the blood of your chosen faction. Revelations is the only one that kinda curbs this by you telling both sides to get bent, but the problem with this is both sides awkwardly agree to team up with you in a very narratively forced way that doesn't really feel organic. It technically has the best ending, but it doesn't really give you the character development to give it a solid, full filling experience.