This manga is perhaps the ideal blend of shounen and shoujo. You have a lot of the traditional shounen elements, like tournament arcs, "power ups", converting enemies into allies with the Power of Friendship™, and EXTREME KOTO PLAYING, but the art is very shoujoesque, as is the focus on interpersonal relationships over the actual battles (they've only had like four major performances in the more than ten years the manga has been running). Taken together it all makes for a really engaging read that's better than the sum of its parts.
My main criticism is that the romance feels shoehorned and repetitive; every so often Kudou will accidentally brush Houtsuki's hand and she'll get embarrassed and cause drama and it'll get resolved and then they'll do it all again a few chapters later. Even now that we finally have some progress we immediately go into tournament mode and the whole thing is basically ignored. Not to mention the combination of good old homoerotic shounen energy and the shoujo art with profuse blushing and talking about feelings makes it feel like it'll veer off into Kudou/Kurata territory at any moment. Oh well, at least Kurusu's kyaa-kyaaing over Kurata is cute. The true galaxy-brained ships are Sensei x Akira and Isaki x Takaoka. Fight me.