Note: This is a SEQUEL and will include spoilers for the first season.
The story takes place shortly after the ending of the first season. The Hoshiijiro ena has been "moved" and early on a lot of backalley type set up goes around to make the viewer question the motives of certain characters. Besides all this the other main focal point of the story is a big one, and quite literally at that since it's the hybrid, Tsumugi.
By itself the story is not anything special, but it has set itself up to have some pretty stunning resolutions and encounters down the road. Watching the internal conflicts unfold within the show is almost as interesting as watching the huge space battles. The show does a really good job at keeping you surprised. It does also telegraph some short term things like a part where Nagate is fighting a group of Guana and he runs out of ammo and you just know what's going to happen, but it doesn't make it happening any less awesome.
Most of the main cast has not changed much from the first season and maintain their stock personalities. Tsumugi is obvious addition and is essentially a little girl with the body of a super monster. Her actions are clearly driven by her instinct to protect those around her and because of her curiosity. The show goes out of its way to really paint a full picture about Tsumugi and it does a good job, although at the expensive of the other characters.
Again the majority of the cast does not change much, this includes Nagate, who is still "the good guy" and Kunato who is still "The Schemer". However, this does not mean what they do is not entertaining. Kunato, who I found to be a glaring issue in the first season has brought a lot of intrigue to the second.
One of the real draws of the show are the battles. They are massive. It's rare for an anime to do something and make me think "wow, that's cool." The animation and art work during these sequences measures up to some of the best there is. However, some of the issues with the CG from the last season remains, especially awkward sluggish movement that makes no sense at all. It makes it very difficult to suspend your disbelief when there is sometimes sudden shifts in animation quality almost instantaneously.
There is a good balance between the tense action scenes and the more simply relaxing parts. I'm glad it didn't try to really be melodramatic about things and it tends to resolve smaller issues that arise within an episode quickly, while using them to build the major plot points they established for a better climax.
Speaking of those relaxing scenes. There is probably debate over whether those comedy segments with Tsumugi and friends really belong in a show like this where they are in constant danger of being wiped out and are humanities last hope and all that. However, I say that these segments are where most of your character development and the viewers connection to said characters happens. Again not like there is a lot of development in the first place, but it's those simple parts that make characters real.
The sound production and direction is the best I've ever heard in an anime and I can say this without a doubt in my mind. All the sound effects are crisp and not only fit what they represent but also the mood the scene is portraying as well. The music is also stellar as it fits whatever scale the show is currently running at. I know I often tout that good sound is sound you don't notice (because that means nothing is wrong with it), but great sound is sound you remember. You remember this.
Knights of Sidonia S2 is a huge surprise for me especially after what I considered a middling first season. However, the production value, overall chemistry of the cast, and just plain enjoyability has skyrocketed. This is clearly worth the cost of admission (seeing the first season) to get the full impact.