Senki Zesshou Symphogear, Venus Project: Climax Recommendations
Both anime feature girls who sing to unleash power and battle. In VPC, the characters are all idols, while only some characters are idols in the Symphogear series.
I can say with conviction that any fan of Symphogear would get at least some enjoyment from Venus Project, as rough and short as it is. From the power and passion of song, comes pseudo-mechanical combat. There is a similarity in aesthetic and feeling as well.