Once upon a time, two brothers passed the happy days of their childhood by studying alchemy, which is governed by the equal transfer principle: an eye for an eye -- you can't get more than you give. But these brothers tried to defy that law, and a horrific accident resulted. Now, the older brother, Edward, is called the Full Metal Alchemist because of his metal limbs, and the younger, Alphonse, is a soul without a body, trapped within the confines of an automaton. Together they search for the power to restore themselves, to find the lives they lost so long ago...
Tales of Vesperia uses the old "Dog of the Military" idea where someone is considered restricted by their orders. Yuri and Ed both follow their own instincts in order to do what they think is right. If you like the idea of watching characters break past boundries and over come odds then you'll enjoy both of these.
Rhiannon is the fair and gentle daughter of a village chief. Unfortunately for her, she's also exactly the sort of maiden who is needed as a sacrifice to wake the Demon King Arawn from his thousand-year slumber and is soon kidnapped for this very purpose. However, when Arawn is summoned, he decides to spare Rhiannon's life, instead killing her captor and freeing her from mind control. Taken with his kindness, Rhiannon immediately decides to marry the Demon King, making him the new village chief. All of this is bad news for Rhiannon's protective but hot-headed brother Arthur, who must now pledge his knightly service to his new Lord, Arawn. Together the three of them must journey and together they must fight, encountering new friends and new foes along the way.
Both of these are medieval fantasy anime with plenty of battles filled with swords and magic. Although Tales of Vesperia is much better, the shows share a similar feel and fans of one might enjoy the other.
The Nation of Gallia has always remained neutral in conflicts and has only gone to war to defend itself. However, as war flares between the East Europan Imperial Alliance and the Atlantic Federation, Gallia is soon targeted for its abundance of ragnite ore, a versatile and hugely valuable material. The Civilian Militia is soon called into action, and Welkin Gunther - son of a legendary war hero - is named leader of Squad 7. Under his command are the headstrong and practical Alicia Melchiott; the sharp-tongued Brigitte Stark; the grizzled veteran, Largo Potter; and Welkin's adopted sister Isara, whose Darcsen heritage means she faces prejudice, even from members of her own squad. With the rest of Squad 7 and the mighty tank Edelweiss, they must do their best to defend Gallia.
Both of these anime focus on a military squad, and have a similar feel. Members bond and characters develop during peace, but there is plenty of action when they need to fight. They are both also based off a video game.