I would like to learn more about the games; I've tried one Advance Wars game a little bit, but, never really had the time to pick it up back.
What were your experiences with the game?
Considering you're big into Fire Emblem, you should have no problem getting into Advance Wars. They're kinda the same thing.
Yet, their difference is the same as between chess (Advance Wars) and a fantasy board game (Fire Emblem). FE is more complex in nature, with many factors to consider that could out of your hand. Advance Wars is much more simple, and every single thing in the game is in complete control between you and your opponent. There's virtually no luck, if you lose a unit, it's your fault.
Advance Wars is probably one of the closest video games to chess. It's very, very simple to understand, but it's incredibly deep due to how much influence you have.
Someone actually made an article having different strategies in chess and then applying it to Advance Wars. Give it a read to get a basic idea.
Best thing about AW (Dual Strike aside) is how units are incredibly balanced. Even the infantry, supposedly the weakest, is arguably the most important. It's because there's so many situations where each unit could be useful, and in those situations there's a possibility even the strongest units are useless, which isn't uncommon to see. Every unit is useful for a myriad of things. As an example, the anti-air isn't just to counter aerial units, it's also very fast (long movement range) and deals significant damage to any units that are weaker than a tank, so it's very very useful early game to dish out quick damage. Only thing that are unbalanced are the COs, but they're only borderline broken in AW2 and Dual Strike. Even then, COs don't determine the game, far from it. Like I said there's just too many situations to consider, which kinda makes them balanced from that alone.
Give it a go. You'll be surprised at how deep it is. Who knows, you might end up finding FE shallow in comparison like I did. lol