Senki Zesshou Symphogear is basically Vividred Operation with more plot and a far darker tone to it. Both series are seemingly inspired by Strike Witches.
Symphogear is more musical and dark with more dynamic characters however it's animation is somewhat wobbly.
Vvidred Operation is basically Symphogear light with a more broken plot and a amount of pacing problems. Only watch Vividred Operation after Symphogear if you are looking for some MOE fanservice without a deep plot.
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.
AKB0048 and Symphogear with have girls singing and fighting. AKB0048 focusses far more on the singing and adds dancing while symphogear focusses mostly on fighting. Both have strong sci-fi elements. AKB0048 more so than Symphogear. If you liked the singing in Symphogear than check AKB0048 out, if you liked the fighting in AKB0048 check Symphogear out, if neither of these apply than don't bother with the other.
In a world known as Soul Shell, floating islands are mankind’s only protection against falling into oblivion. The power of the song is able to heal wounds and create miracles; a power that the young Aurica can’t seem to master. After his ship crashes, Aurica finds herself in the company of Lyner, a fighter who desperately needs to return to what’s left of the sky. Together, the duo set out to find an engineer who can repair Lyner’s ship; but monsters are afoot! With shifty engineers and fire-breathing beasts in their way, can the two manage to stay alive?
Both series revolve around young girls who fight using the power of songs and as expected they both have fantastic soundtracks. Story wise the two shows aren't really similar due to Ar Tonelico being a single OVA based off of an RPG but fans of the OVA/game should check out Symphogear; while Symphogear fans should test out AT's ova and possibly move onto the original game as both series carry the same theme that any conflict can be solved with words alone.
One clear festive evening, Lucia, a mermaid princess, rescues a young boy from drowning. With him, she leaves the source of her beautiful singing voice: a pink pearl necklace. Several years later, Lucia has grown into a young woman, and embarks on a quest to the human world to reclaim her pearl and find her lost love.
In the future, a devastating event known as Second Impact has destroyed Tokyo as we know it, giving rise to Tokyo III - a city under siege by mysterious lifeforms known only as Angels. Mankind's only line of defense are the Evangelions, a set man-made machines piloted by a trio of fourteen year-old teenagers, Rei, Shinji, and Asuka. The fate of Japan and the entire world now lie with these three children, though they might not have the power to save the most important thing of all: each other.
Both of these shows have a similar plot; they're about children who are chosen to help fight against monsters that are attacking Earth. Although Senki Zesshou Symphogear has a slightly more magical-girl feel to it, and isn't nearly as good, their battles still remind me of Evangelion.