Why do some age fans call 3 and 4 archaic then
FE3 lacks many of the features added by later games, so it's very basic. It does have most of the core of the series already though, aside from the weapon triangle (unlike FE1 which has many gameplay oddities) and a fairly unique feature that was mostly forgotten afterwards (mounted units can dismount, changing from lances to swords, and
need to dismount for indoor maps). Compared to FE7, it still has villages, shops, arena, the intermission where you can swap equipment before battles... So a lot of the game would be familiar, but it's missing elements like battle sprites following the color pallet of the portraits, supports (there are some built-in character relationship boosts, but no support conversations), characters who still appear in story scenes after joining your party (they all basically disappear once joining as playable units outside of Sheeda/Caeda participating in many recruitment conversations), alternate objectives are also kind of missing, but not really (you need to conquer a throne/keep to finish almost every chapter, but many chapters especially in book 2 incorporate design elements that basically force alternate objectives, especially if you want all to get all characters and the real ending).
FE4 introduced the weapon triangle, skills and generally has all around better graphics than FE3 alongside faster and more dynamic battle animations. There's also a core cast that actually keeps story presence unlike FE3. You can pair up characters like in FE7 (but only for romance) and some get conversations, although only for specific pairings. However, it has some odd design choices, like characters being unable to give items to each other. You need to resell them to a store and buy them with another character, since each one has their own funds.
Some people dislike the basic premise of Conquest's story - basically siding with the "evil" side of a war just because the family the main character grew up with is there, while attempting to keep their own hands clean, but not actually stopping evil atrocities from happening. On top of that though, a big part of the later plot of the game is entirely reliant on clumsily implemented plot devices rather than natural development.
I actually like the basic premise, but the execution is just stupidly done at various points (although I think some script edits could fix many of the issues, which frustrates me due to them changing supports and some light-hearted story dialogue quite a bit in the localization but largely avoiding actual story plot points).
