Toaru Majutsu no Index, Guilty Crown Recommendations
A boy meets a special girl and finds himself dragged into a world of danger that he previously didn't know existed. Both boys, Touma and Shu, find themselves fighting against an enemy to protect something. Great art, great characters, great music.
Both worlds have a similar feel that draws you in. As they say: "when science and magic meet... They will beat the crap out of you."
Although I'm not sure if there's magic in Guilty Crown yet.
Both show the protagonists fighting against a corrupted government obsessed with power and control. The main male protagonist also has special 'powers' in his right hand in both Animes.
In each anime a boy holds a power in his hand that can change the world.
The leads' right hands hold superpowers. Index is so much better though.
these two anime has a mix of the slice-of-life, supernatural and some sci-fi genre in it. You won't be surprised to find in both of them, a protagonist who's goal is to 'do what's right', along with save and protect the one's important to them.
Both protagonists are males who you'll see first starts off as nothing but dirt, but eventually starts to develop the strength and courage to become the hero they try to be in the story.
MC has special power on his right hand, which he uses to fight evil that lurks within the upper powers that run the city. MC also meets a girl that inadvertently drags him into life-threatening situations because of the importance of said girl.