Advance Wars is more dynamic, quick and, instead of watching an individual battle between two archers
And of course, AW builds up strategical reasoning better than FE. So, instead of leveling the character with the best base stats and build to fight with him/her alone, you can build up an entire army (which means spending money) to conquer enemy territory by using your brain alone (and of course, if you have the top guns, it means you have territory.)
Of course, they are similar games from the same company, but Advance Wars provides a better gameplay than Fire Emblem. Still, you can love Fire Emblem a bit.