As someone who loves Advance Wars and isn't big on Fire Emblem, I disagree with the assessment that Advance Wars is just "a modern Fire Emblem." I was actually in the process of explaining all of the differences, but then I realized just how insanely long that would take... but the main thing I love about Advance Wars is that it is a great multiplayer game, whereas Fire Emblem's multiplayer pales in comparison (and in a lot of FE games, seems like more of an afterthought).
I guess some general things to mention are that I feel Advance Wars is based more on strategy whereas Fire Emblem is based more on luck; Advance Wars focuses more on the gameplay whereas Fire Emblem has a lot of emphasis on story and characters; Fire Emblem consists of less, but important, units in battle, while Advance Wars is more about a big army of unidentified units; Fire Emblem combat mostly takes place on land and some air, while Advance Wars is almost equally about land, sea, and air; and with Advance Wars, you can do big multiplayer battles on a big screen, whereas with Fire Emblem they have to be linked (and I'm not sure any of those support more than two players).