Yoku Wakaru Gendai Mahou

Both anime are about girls who use magic. In both of them they talk about sacrifice and world´s destruction. The protagonists Koyomi and Madoka are very similar, also Misa is a bit similar to Mami and Yumiko to Homura. In both of them people go back in time. At the end two girls fight for their friendship. 

1: Both series deal with having special powers. 2: The protagonists Koyomi and Hibiki are very similar, they are clumsy and willing to help others. 3: The creatures they fight are similar too. 4: Tsubasa is a bit like Yumiko. 5: And they also both have action and drama and give importance in human relationships. 

Both anime are about girls who have special powers. In both anime the protagonist thinks of her power as something bad. Also in both of them the girls become good friends. 

Koyomi is similar to Yumi and Yumiko is similar to Sachiko. In both stories relationships between girls are shown. And apart from that in both of them there is an episode in witch a character does not know how to eat a hamburger. 

Both series deal with the innovative and modernized version of magic. In both Gendai Mahou and To Aru Majutsu, different schools of magic are presented, from ancient magic to modern magic.  

Both series deal with modern day mages. While Mahou Tsukai deals with magic with a more "realistic" way, Gendai Mahou clearly exaggerated the effect of magic. However, both involves young students studying under a master.