Macross F, Senki Zesshou Symphogear: Meteoroid-Falling, Burning, and Disappear, Then... Recommendations
Both fighting with the power of songs.
Although macross is more set into space then Senki
They feature a lot of songs and music is central to the plot, as it amplifies people's fighting abilities.
Girls. Fighting weird creatures. By singing.
Both animes use music, singers and idols as a way to fight in the world that they are living in, whether it is to survive or for power/hope.
I was lucky enough to watch Macross Frontier after starting Symphogear.
For those who wants something with dynamic fights and singing chars I recommend Macross Frontier. MF is just far better in production. You may miss Symphogear's clumsy madness, but MF is all about perfect quality.
Similar style involving girls singing to music and fighting the good fight. However, Senki focuses more on action/drama while Macross Frontier has that love triangle side. Both series have great soundtracks.
Both anime fight alien-like enemies.
Both series also have idols who fight.
Both series are sci-fi
Both have awesome soundtracks :D