Far in the future, humans have begun to live in space colonies and interstellar travel is the norm. This epoch is home to Akiha Shishidou, a daughter of the wealthy and powerful Shishidou family. She is a girl with no ambitions and seemingly no direction, until she bumps into Leopard, an obnoxious, arrogant and slightly crazy "brain colony." Soon, Akiha is enlisted by an enigmatic young girl named Honoka to steal some parts for Leopard, and her life becomes filled with danger, excitement and the occasional run-in with the Inter Colony Police. Akiha must work to reassemble Leopard in the midst of conflict and in the face of a mysterious malevolent force lurking in the shadows. Is she really, as Honoka says, "The Girl Who Leapt Through Space?"
These two sci-fi comedies have a lot in common. First, they're really similar visually with lots of bright colors and moe'ish artwor. Both series also feature a large cast of fun and original characters. Sora o Kakeru Shoujo's production quality is much higher (thanks Sunrise), but both shows should please anyone who enjoyed the other.
Similar tones and themes. They feel very similar to each other, in addition to the fact that both take place in space and feature attractive (YMMV) females saving the world. Kakeru shoujo does have higher animation quality, but both are very good, and I strongly suggest anyone who likes one to watch the other.
Guided by a star only they can see, a group of maidens known as HiMEs have begun to gather at Fuuka Academy. These young women have been endowed with dangerous supernatural powers that they can use to their heart's content, but there's a price: to wield them, they must put their most important thing on the line. Now, in the midst of school work and friendships, they find themselves caught in the midst of strange conspiracies seemingly related to the terrifying monsters that attack them. Is the power of the HiMEs strong enough to save themselves and the ones they love?
This is more of a gut feeling rec; they feel similar even if their context isn't. Both revolve around girls (who happen to wear similar outfits), and are slightly futuristic. If you're a fan of one, I recommend giving the other a try.
Simon lives a boring life in the underground village of Jeeha, where his main job day in and day out is to dig tunnels. His close friend Kamina, however, longs to bust out of their oppressive existence and reach the surface world where open skies and adventure await! One day, during his usual digs, Simon discovers a robot with a big face buried amongst the rocks. No sooner has he shown Kamina his mysterious find when two beings from the surface crash land into Jeeha Village - one is a gun-toting woman calling herself Yoko and the other is a terrifying mecha piloted by a Beastman! Seeing their chance to escape village drudgery, Kamina rallies Simon and Yoko to defeat the invader using their new robot, Lagann. However, upon breaking out onto the surface world, Simon, Kamina, and Yoko encounter enemies more powerful than they could have envisioned. Their fight for adventure just turned into a war for the survival of the human race - will their lust for freedom hold out against such terrible odds?
Both shows are very, very similar in the sense that they both are pardodies of their own genre, and both have a very solid (and massive) cast. In both cases, each character is important in its own way, and most of them are present in each and every episode. Pick your favourite and follow them through the end. If you like the comedy value of one of these two shows, I'm pretty sure you'll love the other so give it a try!
In a far and distant future, men and women have become mortal enemies. Each living on seperate planets, an interstellar war is being fought between the two very different peoples. Hibiki, a mere 3rd class worker, finds himself in the middle of a huge space battle, facing the nemesis of mankind: Womankind!
I was reminded of Vandread while watching this. Although not extremely similar, they are both mecha anime with an almost total female cast, and the mechas are able to change into a different form. They both also take place mostly in outer space.