Senki Zesshou Symphogear, Cross Ange: Tenshi to Ryuu no Rondo Recommendations
Similar art style. Both anime feature a female protagonist and use singing as a way to activate their powers.
Both have a mixture of music, action, sci-fi, fantasy, and yuri. If you liked Nana Miyuki's insert songs from Cross Ange, you get more of that in Symphogear, as well as another badass character that undergoes a lot of growth voiced by her. The lead is not Nana's character, but rather Madoka's seiyuu from PMMM, who delivers a stunning performance in her own right.
The concept of applying music to engage in battle is a primary theme of Symphogear, and the insert songs and OST really shine. Both feature plots that aren't necessarily the greatest (I'd say Symphogear's outperforms Cross Ange in that department), but