I enjoy Advance Wars more on a sheer strategy level, but it's story and characters are very silly. Especially since many hundreds of soldiers die in the ridiculous story.
Fire Emblem is a Strategy RPG and in addition to some of the best strategy I have ever played in a SRPG, it has great story and characters.
It is somewhat frustrating, since all characters who die are gone for good, but it adds a nice level of challenge missing in many SRPGs (Vandal Hearts 1,2, Kartia, FF Tactics Advance, Front Mission 3, Tactics Ogre Gaiden, Arc the Lad, Shining Force).
It is easily my favorite game of last year, even though it took me well into this year to win it.