As a young boy, Phoron met a spirit named Corticarte Apa Lagranges after she heard his song one night. Now, twelve years later, Phoron attends the Tolvas Commandia Academy, where humans train to become Dantists – people who can control spirits with music. One day, while unsuccessfully practicing a melody, Phoron sings the same song from all those years ago and not only does he manage to summon Corticarte to his side, but also makes a contract with her! Now he is bound to the temperamental spirit and, alongside his friends, Phoron must learn exactly what it means to perform a Commandia. But with a dark threat approaching, is it possible that this hapless orphan could actually be the key to preventing disaster?
The story of Yu Himura and Yuko Amamiya’s relationship is troubled and complex. One day, Yuko showed up at Yu's high school and, despite the two not having seen one another for ten years, confessed that Yu was her first love and still loves him. In the present, Mizuki Hayama moves in with her cousin as she prepares to begin high school. She meets his smooth and handsome neighbor, Shuichi Kuze, and begins spending increasing amounts of time with him; they begin to fall for one another despite their age difference. The tale of these relationships thus begins to unfold.
Both anime have beautiful animation. (ef slightly moreso) Both have a dependancy on music to tell their stories and the characters are suprisingly similar considering they are faced with many dilemas. The biggest difference of these 2 are the plots. ef - a tale of melodies is heavy on drama/romance where Shinkyoku Soukai Polyphonica Crimson S takes the world in a fantasy direction with interesting powers and conflicts. This is kind of a gut recommendation here but if you liked one i highly suggest checking out the other.
As an orphan whose life is in the hands of space pirates, Coud has had no choice but to survive on bravado alone. He has nothing to live for until he finds Ren entombed amongst the treasures in the pirate ship's hold, and awakens her. In addition to being mysterious and beautiful, Ren can transform into a battle sword to help Coud fight and prove his strength -- but with this strength comes the bitter realization that power alone is not enough. Now, in a race against time, Coud must endure betrayals and fierce battles as he struggles to return Ren to her home, before it's too late...
Fantasy world? Check. Girls and spirits with magical powers which need a contractor to be used and are activated through songs? Check. A decent dose of comedy? Check. Romantic elements? Check. Good music (more in Crimson S than Elemental, but you got the point)? Check. Some cool fighting scenes? Check.
There may be even more similarities between the two series, but these are the most noticeable. Keep in mind, Elemental Gelade is much more action/adventure-oriented, while Crimson S has a slower pace and focuses more on the characters' relationship and background, but I think if you liked one you should at least give a chance to the other.
One last thing, Crimson S is a prequel to the first SSK, so you don't have to watch it to understand the story.
Both series have girls (and some other beings) who fight using songs and their power varies according to their feelings. The setting is quite different, but they share the similar tone, how they reveal the plot points, the themes and the shiny battle scenes. Symphogear is much more exaggerated in what it does, and that's why I personally prefer Polyphonica, but should you like one, I suggest trying out the other.
In a world where magic is a reality, the young Louise is at the bottom of her class. Dubbed "Zero" by her classmates at Tristein Academy (due to her zero success rate for magic), Louise (along with all first year students) was charged with summoning a familiar; and instead of a cute magical creature, the familiar arrived in the form of... Saito Hiraga, a normal Japanese boy who was abruptly teleported from his own world?! Can both Louise and Saito come to terms with their new and complicated "relationship" and (more importantly) help Saito find a way home?
Both ZnT and Crimson S are set in schools which are different from the norm and teach more fantastical subjects. Both also feature people teaming up with spirits or magical creatures. If you enjoyed the fantastical element of one, then you may well enjoy the other.