So I've never played FE:Aw (what kind of
Robin lover am I right?) but I love Fire Emblems in general. I beat the first one on NES, Gaiden, and Radiant Dawn and played partially some others. RD was -ok- but it seemed it lacked a certain strategical oomph from the earlier ones. Does Awakening carry on the Fire Emblem legacy admirably or, like many game series, does it start to fall flat? (I'd prefer the opinions of those who've played multiple FE's but any input is appreciated

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As someone who's played several FE games, I'll give you a quick overview. You have access to classic and casual modes, which basically let you decide wether you want the traditional permanent-death mechanic on or off, and the ability to save mid-battle. Casual mode can allow for a more relaxed experience. The game looks good and has a good soundtrack. It also features (quite decent!) voice acting. Characters don't have a limited amount of possible level ups anymore due to the second seal, which allows characters to switch classes when some mild conditions are met. This does allow for a personalized playing experience, though. For that matter, you can also grind in between chapters if you like, by random skirmishes or DLC chapters. This game excels in replay value compared to other entries in the series.
The story isn't anything spectacular, but it has its moments. DLC is not part of the main story, though a few DLC chapters provide additional backstory. The character roster isn't as massive as most past games, but the characters are definitely deeper and more interesting than before thanks to the support conversations and the frequency at which they are unlocked. Characters, including your avatar character can even marry. What that results in... well, that would be a spoiler. But if you get the game, definitely go for this. I can tell you it unlocks additional chapters.
In general, the game is better than most past games, and it's very enjoyable. The game does take a hit in a specific area, though. The gameplay. All maps are route enemy or route boss enemy. The map design is also rather poor. You will likely find that simply overpowering your foes is often more important than strategic positioning, which is the result of some poor design choices which you will probably notice upon playing.
Still, the game is very enjoyable, and I strongly recommend it despite the complaint just above. As a Fire Emblem game, it is very good, just expect a few letdowns. A quick tip: be mindful of your grinding. This particular entry truly is as difficult as you want and decide to make it.
On that note, also consider Path of Radiance (for Gamecube) if you can get your hand on it. It's my personal favorite in the series and I'd recommend it to anyone. It's the prequel to Radiant Dawn, btw.