Really popular VNs tend to get reissued for PS2 or PSP with all the sex removed and sometimes additional gameplay elements added.
Part of Muv Luv's popularity is that the various parts of the game involve putting a standard VN cast of characters through multiple genres. The first third of the story is the "traditional" one and resembles other vanilla datesims like Kimi ga Nozomu Eien (made by the same developer, IIRC). There are hints of something strange happening, though, with a lot of conspicuous references to mecha anime and some inexplicable plot events occurring.
The second part of the story concerns the main guy ending up in a parallel universe where he and his friends are all fighting aliens in giant robots. Where the first part was light and goofy, the second part is extremely straight-faced and super-detailed. You don't actually see the aliens, the emphasis of this portion of the story is on how all the characters are different and what the shape of the world is. This is also the part of the game that is generally considered the best.
The third part is actually an entirely separate game with much higher production values where they can afford to show us some alien-fighting. This part of the story is written in homage to the violent and nihilistic mecha anime of the early 80s, typified of directors like Yoshiyuki Tomino and Ryosuke Takahashi. All but three of the main characters die brutally, some with gory "death CGs" that actually offended the Japanese playerbase.
Unlike most VNs, this part of Muv-Luv is totally linear and it's impossible to save any character who dies. A lot of the emotional impact of this comes from playing the first two games, where you see the characters as they'd be in gentler stories. Alternative also circles around to the first third of the story at points, eventually explaining some of the strange things that happened.
Much of Muv-Luv's popularity with Japanese players comes from the way it combines the primal otaku-beloved genres of harem and mecha to draw out maximum emotional impact. I don't know if the game will affect a foreign player who didn't grow up on a steady diet of giant robot shows in quite the same way. It's probably worth your time if you're curious and if you already know you enjoy stuff like Fate/Stay Night and Higurashi.