I heavily anticipated Fates when it released and was very disappointed with it.
I've played most Fire Emblem games, including the Japanese only releases, and some of the aspects that didn't seem to carry into Fates were good worlds, a likable protagonist, good map design, and a passable story.
As a whole, I've always felt like Fates focuses more on it's features that aren't characteristic of other Fire Emblem games. Where it does focus on its traditional strategy-RPG gameplay, I think it mostly holds up. I do think a large portion of the maps focused on bad gimmicks and I always felt like the enemy stat balance was off (without grinding, my units just couldn't take more than one hit without dying), but the skills and weapons were a fun change, even if I prefer traditional weapon durability.
However, the story was not only boring, it was sometimes very hard to read. I've often said the story-writers probably wrote a good bit of the story before deciding on the three-path option because the tap-dancing the story uses for Corrin to justify taking the Nohr route seems very forced since Nohr is just the "evil route" in my eyes. Fighting for Garron just feels like taking the objectively wrong choice. Birthright is definitely the best in story and Revelation wasn't horrible, but the story definitely had more potential and I don't think it was the right one to try to implement a "three choices" concept into.
Characters were overly cliche in so many ways, so much that very few stick out in my mind years later. Corrin follows the trend of being very boring, presumably so the player can relate more to them, but even compared to Robin and Kris, Corrin is verrryyy boring. Most support conversations that happen between two characters that aren't Corrin are fine I guess, but any of Corrin's supports just don't really do much for me.
All this boils down to a game that doesn't really hold any replay value for me. Sure, some of it's maps are pretty good and if you just ignore the story and characters, it's pretty fun to just play. But all of the aspects I mentioned above can be found in better forms in so many other games, so I have little motivation to go back to it.
The art and character designs are pretty good though, I think they look mostly better than Awakening's.
If you're still looking to play some of the older games, you can't go wrong with the GBA games. My personal favorites are the Japanese-exclusive "Thracia 776" and "Genealogy of the Holy War" but it's kind of a commitment to get into those. Still I highly recommend any of these if you're looking for better characters, a better protagonist, passable writing, and good maps.