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.
In both shows, girls with superpowers use mechanical summons to engage in battle. The fighting is more organized in VPC (tournament style) than in Mai-HiME (they don't know when enemies will show up, and they must be prepared to fight on the spot)