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On the whole both take place with a 'medieval fantasy' setting. Plot-wise they remain difference, but there is a similar feel in a 'save the world' way.
Male and female lead who are both very capable (and the female being relatively terse characters).
Legend of Legendary Heroes focuses more on political intrigue.
The power to cross over dimensions is one that is deeply coveted -- a lesson that childhood friends Sakura and Syaoran learn the hard way when an unknown enemy attacks an archaeological dig in their country. As a result, Sakura's memories are scattered to different dimensions, causing her to fall into a deep sleep. In order to save Sakura's life, she and Syaoran must journey to various worlds in search of her memories, with the help of fellow travelers, Fai and Kurogane. But finding Sakura's memories won't be easy, and the price for traveling through time and space is high...
Death and reincarnation are inescapable, but what happens in between? Without warning and without his memories, a boy who only recalls his last name - Otonashi - wakes up next to a girl named Yuri who offers him a gun and tells him to shoot an angel. Assuming it must be a misunderstanding, Otonashi is then almost killed by the angel and is drawn into Yuri's army to battle to delay the beginning of his next life. Immortality is within reach, but if Otonashi remembers how he died, will he keep fighting or allow himself to vanish?
The fact that characters are stuck in a game-like world which has a specific set of rules made me think of Sword Art Online when watching Angel Beats!. While those two series are not exactly similar, I believe that this feel is enough to justify a recommendation.
Additionally I would like to add that both series sport a competent male lead (I'm not sure if this is the right word to describe them). Simply put if you liked the male lead in one series, you shouldn't be disappointed with the other series.
In a mystical land filled with magic and monsters, eager adventurers scour a ten-floor dungeon in search of fame and fortune – if they are able to escape with their lives! But none dare set foot in the tenth floor, as a powerful foe will make sure that they never return to the light of day: the evil Werdna, a wizard who stole an amulet of immense power. Now, to aid a beautiful woman, a group of skilled warriors must descend to the tenth floor to find the woman’s lost love, and to take back the amulet from the hands of evil!