One thing I prefer about Fire Emblem over other strategy games is that each side moves all of their units in one phase. The more common approach used by a lot of isometric strategy games gives each unit an individual turn, and I find that makes it more annoying to coordinate strategies, especially when there are techniques to mess with the turn order.
I also like how progression is retained between maps, and I keep the same units throughout the campaign. I could never get into Advance Wars whenever I tried because I find it annoying that you often have to start from scratch on a map, build up money and buy units (and while your opponent starts with a lot of units). And the maps where your opponent has access to factories can break down into a tedious stalemate where your both cranking out units to keep up with each other, and they die to each other without the game-state changing. And I have the same problem getting through the campaign in RTS games like Starcraft where I have to redo all of the research and whatnot that I did on the last map to upgrade my units. So I guess I like the balance of Fire Emblem where the player units are a significant force in their own right, and the enemies are weaker. But the tradeoff is that losing a unit is a significant loss to the player to the point where the enemy can throw several units at the player just for the chance to take out a single player unit, and the exchange would be worth it.