Shinkyoku Soukai Polyphonica Crimson S

Both are about humans being able to control spirits to fight for them. 

Both of them have music and fantasy creatures that love music. Also the main characters can't play music and have to try harder in order to find the correct way of playing music. 

As with the first installment, the second in the Polyphonica series relates to Symphogear in the music department. Both series use music as their source of power to fight. 

Both of these animes deal with a main guy and how well he is doing at school along with the girls he is with.  

If you liked Polyphonica, you'll probably like Shana too. They are both very similar animes, although they have their differences too. Although, the main characters of both have crimson hair. LOL. And have the same kind of temper. Tsundere. 

Both have mystical beings. Horo is high-classed so is corticarte 

Both anime are about people contracted to supernatural beings. In Polyphonica we have a man contracted to powerful spirit with not so noble past, in Chrno Crusade we have a girl contracted to powerful demon-made-good. Both anime also have the same theme about stopping others like them (contractees or demons) from their evil schemes. 

Both anime take place in school related to magic (pure wand style magic in ZnT and songs to command/strenghten spirits in Polyphonica). Both have pairs contracted by magic (a mage and human familiar in ZnT and human with very human-like spirit in Polyphonica). Diffrences include: Znt is set in medieval-style magic world, while Plyphonica in alternate world with modern technology and spirits living alongside humans. ZnT is also much more harem/ecchi style. Moreover ZnT lacks definite ending, even if we include the other 2 seasons. 

Both Male Characters (Oz - Pandora Hearts and Phoron - Shinkyoku) encountered a Girl which hold a Mysterious powers. In Pandora Hearts, Alice is a Monster or a Chain while in Shinkyoku, Corticarte is a Spirit. Both Male Characters are able to command or give orders to those two girls. Also Both Male and Female Characters have Romantic feelings towards each other. And Both of them have Comedy which the Main Female is always like a Tsundere type. 

A chibi/younger version of the female protagonist is bonded to the male lead and only in special circumstances changes back to their original forms.