Despite the cold, heartless rigidity of grid and number-based combat, Fire Emblem has been able to connect to players through its many colorful characters and their interactions. More than any other game in the series, relationships and romance are truly at the heart of the recently released Awakening, making it the perfect "romantic" game for this Valentine's Day.
The extent of romance in FEA is basically, "You baked me a pie! It's awful/delicious! Marry me!"
Bottom line, I love what they did with relationships on the battlefield and REALLY hope they continue to expand on it in future titles.
What I'm saying is that, while yes, it does add a lot to the game, it's not technically impressive and doesn't really offer much depth.
It's a great sub-feature, don't get me wrong--but it's just that, a sub-feature. The real meat of the game, the point where they really spent all their time and effort, is the combat system. Not the narrative, not the characters--the combat.
Off the top of my head, I can really only think of one game that offers unique & in-depth relationships between NPCs, and that's Baldur's Gate II... thanks in large part to decades of scripting work by fans.