Senki Zesshou Symphogear: Meteoroid-Falling, Burning, and Disappear, Then..., Kill la Kill Recommendations
Symphogear starts out a little slow, but I believe if you like Kill la Kill and singing/music, you will almost certainly enjoy Symphogear. Symphogear has battles that get on a level of hype near to Kill la Kill's final battle. Both shows have awesome transformation scenes (Symphogear's gets improved after first season). While it is a lot of fun, it also has its serious moments.
The most important thing: I loved both of their OST's. They fit the action very well, and reflect the state of the character's feelings in the particular scene.
If you like Kill la Kill but thought it could use more singing, then Symphogear is the anime for you. If you can't stand the first season, the second is generally considered much better.