I believe that I read that Sora wo Kakeru Shoujo is supposed to be a “spiritual successor” to the My-Hime series.  When I think of “spiritual successors”, my first thought is usually how Fallout is a spiritual successor to Wasteland.  There’s no continuity between the two, but some kind of similarity in theme or setting to make them “feel” similar even though they’re on different planes.

(so like, are we supposed to call it "sora kake girl" or something?)

Sora wo Kakeru Shoujo has some staff in common.  A lot of the voice cast is the same, and both series have the same character designer director.  The most important difference is that the writers are different, which is one of the biggest factors in TV production.  Tone and themes are a little bit more of a stretch until you dig down a little more.

For example, the settings are different.  The My-Hime shows took place at schools (although one was a Japanese high school while the other was medieval-ish maid-ish school), while Sora wo Kakeru Shoujo is well, all over the place.  Yet while the settings are different, both shows are playing with magical girl conventions (with Sorakake being a more Nanoha-ish sci-fi tack.)  Tone is probably the closest analog.  Sorakake is much more madcap than even the goofiest parts of My-Otome Zwei, but regardless both series have a playful, irreverent tone to them.

The tone is kind of hard to really accurately describe, though.  I’m reluctant to say that it’s parodic (or that the show is a comedy).  Parody, after all makes fun of something and I’m not quite sure what specifically (if anything) is getting made fun of.  As for being a comedy, while the episode was kind of funny and very zany and madcap (it felt almost like Vandread with the fast forward button held down), the pace made it almost hard to laugh at times.  It was so madcap that there was never an opportunity to laugh because they were moving so fast that it’s time for something new.  Jun Fukuyama as Leopold (Leopard?) the Gurren Lagann reject (he totally looks like one of the Gunmen) exemplified that.

(On a side note, it’s like an inverse with part of the problem with the comedic timing in Borat.  I saw it in a packed theater and I felt like I missed half the jokes because everyone was laughing so hard and so long that I couldn’t always hear.)

Random notes:

1) I feel like I had no clue what was going on because the whole thing was going so fast.
2) Tee hee, sci-fi-y magical girl sidekick
3) I kinda/sorta got Otome wa DO MY BEST deshou? vibes from the ED
4) I feared the worst with Masakazu Obara doing the designs since he reuses them constantly.  I don’t mean like how Hisayuki Hirai’s all look the same.  I mean how characters like Lena Sayers and Haruka are exactly the same in both My-Hime and IGPX. Whoopsies!
5) Just looking at the credits now, I see My-Hime seiyuu alumni with Aya Endo, Yukari Tamura, Yukana, Yuka Nanri, Naomi Shindo, and Rie Tanaka
6) And on a final note, wasn’t Idolmaster Xenoglossia also kinda supposed to be a spiritual successor to My-Hime? Sorakake and Idolmaster do share the same writer!