In 2010, the Britannian Empire enslaved Japan using powerful mecha known as Knightmares; in the aftermath Japan was renamed Area 11, and its people began a hard and terrible existence. Lelouch, a Britannian student living in Area 11, has grown up hating the Empire and everything it stands for. One day, in the middle of a terrorist attack, Lelouch meets a mysterious girl who grants him the ability to control minds. Can he use his new power to fight for freedom, or will his hatred twist his good intentions into mindless acts of vengeance?
I don't want to say anything about why I think these two anime are similar, because I don't want to give anything away about the plots of either. But the plots and the overall themes (peace, war, freedom) share some similarities. Everything else, maybe not so much.
Ohana Matsumae is a sixteen-year-old girl with no purpose or direction in life. One day, however, she gets the chance to reinvent herself when her mother and her boyfriend do a moonlight flit to escape his debts. Left alone, Ohana goes to live with her estranged grandmother, but when she arrives she finds herself forced to work at the family’s hot spring resort, the Kissuiso Inn. With her grandmother considering her nothing more than an employee and a roommate who hates her, Ohana’s happy dream of a new life soon turns into a nightmare. Now the wide-eyed girl must learn the value of hard work as she attempts to make friends and familiarise herself with life at the resort.
If you enjoyed Fam as a main character--cheerful to the end, naive/innocent and frequently unaware of others' feelings, and dropped into a situation where she sometimes lacks delicacy or doesn't fully realize the ramifications of her actions but continues trying anyway--you'd also enjoy Hana-saku Iroha, where the same type of main character, Ohana, experiences much more character development over the course of the show.
Kanata Sorami, a young Private in the army, arrives in Seize to serve in the Clocktower Fortress and learn the trumpet under the tutelage of Master Sergeant Rio Kazumiya. Though peace hangs uneasily over the world, Kanata finds a relaxing routine of laundry, shopping, and trumpet practice greets her at her new post instead of brutal drilling and discipline. With help from the other members of the all-female 1121st Platoon, Kanata finds her place in the bustling city, bringing joy and humor to the war-weary residents while learning a great deal about the world.
Both stories are about young/cute/innocent/cheerful girls in post-apocalyptic military-type situations (situations that involve a much larger political backdrop than the characters are maybe aware of), although So-Ra-No-Wo-To is a bit more cutesy-slice-of-lifey than Fam, the Silver Wing.
Akiyuki lives on post-war Sentan Island, always rushing between the demands of his separated parents and his friends at school. But his carefree days come abruptly to an end when his school bus suffers an explosion, the first attack to plunge Sentan back into war. Akiyuki lives to find himself turned into a Xam'd, a mysterious creature, by the suspected cause of the explosion. Engulfed by Xam'd, Akiyuki is eventually saved by a red-haired girl, Nakiami, only to find himself torn away from those he loves. Now he must work to control and understand the creature within him, all while searching for his family and friends in a world steeped in the secrets and chaos of war.
Fam is a very different show from its predecessor, however, I believe that Xam'd is a good recommendation for both Last Exiles. Fam and Xam'd have really interesting worlds, with a variety of countries and settings that affect the people who live there. Both shows also have a protagonist who gets pulled into larger events (politics, war), both have lots of flying machines, and both focus on human relationships.