Both of these shows combine fighting and singing to create a weird mix of idols and action that have more serious plots than regular idol shows. I think if you enjoyed Symphogear you'd enjoy AKB as well, as long as you don't mind that AKB focuses less on action and more on idol activities.
Earth is under attack from otherworldly creatures known as Evolutionary Invasion Objects, and only the agents of DOGOO, a government organization, can keep the monsters at bay. Armed with special weapons infused with the souls of distinguished historical figures, these fighters, recruited by an alien who watched its planet be destroyed by the Objects, are humanity’s best chance against the invaders. Teenager Shio Ogura used to be nothing but a loner and a military otaku, until one day she and her class went on a field trip to Taiwan and found themselves smack dab in the middle of an Object attack. To help save a new friend, the girl picks up a gun infused with the famed samurai Nobunaga Oda, thus securing her fate as the newest member of DOGOO, and protector of humanity!
In each show a relatively normal, if not socially awkward school girl has a mysterious and dormant power that is suddenly awakened. They are then brought into a super secret defense organization that exists to counteract some otherworldly threat.
Both shows like to focus on crazy action featuring their unusual powers. In Symphogears case the powers are all based around music, whereas in Nobunagun those with power are the reincarnations of famous historical figures. But both will likely please an action fan.
Both of these shows are about a group of armoured girls that are almost military style magical girls. Both shows also have strong themes of friendship, and focus on that rather than simply destroying your enemies.
Vividred Operation is the more ecchi of the two series, while Symphogear focuses on music. Both feature characters who are drawn in the same cutesy style, as well as having similar, positive personalities.