Deeper worlds and more ambitious story I'll definitely give you, those games have the best stories in the series by far, but I don't really play the games for story. The gameplay felt worse to me, iirc it was a lot slower and the class system felt like a step down though it's been a while, I also remember some specific stages having pretty annoying maps (especially in RD). The games are still great though.
Awakening being easy to "break," doesn't bother me personally because I enjoy breaking RPGS and being OP, and on my first playthrough I never figured out how to break the game anyways. I like the waifu and anime stuff, however certain characters (Nowi especially) and in Fates the ability to invite your characters into your quarters for no apparent reason is creepy/embarrassing though but wasn't prominent enough to affect my enjoyment of the games. The story in both games isn't very good but it's not like awful, I've experienced much worse. I'd say the vast majority of games Square Enix has released in the last 15 years probably have worse stories. And again I don't really play the games for the stories.
7 being sort of a Mystic Quest doesn't really bother me because I'm not very good at these games anyways. As a kid the games might have lost me without a 10 chapter tutorial tbh since I had a ton of difficulty starting out. I haven't played enough of FE6 yet to judge that game but from what I played it seemed close in quality with 7 anyways.
I'd say Tellius maps are better designed and more varied than the GBA games, with tighter fights and varying objectives. I'd say that the return of the skill system adds to the strategy and tactics. RD has some of the best levels in FE. That is not where it is weak. Its weakness is as an RPG and the story has some dumb points. Beyond this you have moments like the BK fight. Great moment.
FE Awakening is broken on a basic level: You do not need to break the game. The children are completely broken. The pair up system is completely broken. The combat support system is broken. The support bonuses are poorly balanced. Then you can do that whole re-classing thing, but that wasn't even what I was talking about.
FE6 has a better story, better levels, better gameplay, etc. than FE7. A lot of that comes from FE7 being a lazy prequel and being a 'Mystic Quest.'