Crest of the Stars (and it's sequels) has always struck a chord with me. Ever since I first encountered it it has been my favorite sci-fi story but I never knew why. In terms of the basic premise, it's not especially remarkable. A young man and a princess go on an adventure and overcome impossible odds... IN SPACE. However, I believe the charm lies in what it does differently from other sci-fi or space opera.
Let's look at the way it's written compared to other sci-fi first:
A common practice in sci-fi writing is to start the story in medias res ("in the middle of things"). The reader is plunged into events as they happen with exposition being given primarily through flashback or internal monologue. It is also common to start with a prologue and then jump much further and filling in the blanks through flashback, internal mono, or dialogue.
Crest of the Stars does the latter, but in a different way than is common. There is a prologue which illustrates the first important event in the story. The time between the prologue and the first chapter is largely unimportant. A few key facts are established in the first chapter (nameley that the protagonist was in school the entire time and that he made a few friends that he played a baseball-like game with until they learned his identity). The author COULD have chosen the Heinlein route and used the school as an infodump, but he didn't.
Basically, the story is told chronologically. You go from one important point to the next with exposition done primarily through dialogue.
Next, the universe:
The universe of the Seikai series is very deep. The "science" is well established and the politics are extraordinarily well thought out. It even has a unique language. This describes other sci-fi stories as well, but the reason Crest of the Stars is better is because it doesn't force the universe down the reader's/viewer's throat with expository infodumps (at least, not often). Insight on the universe is very stealthily delivered through in-universe literary quotes at the beginnings of chapters/episodes or through passing remarks. Even of one doesn't pay attention to those, the reader is given enough info through superficial clues to understand the situations and motivations of the characters.
A deep universe that can be enjoyed superficially.
This is where Crest of the Stars really shines. First off, besides their social statuses (a count and a princess) the protagonists are largely unremarkable. They have no special powers, no super weapon, no special training (the princess has had basic military training, but she is by no means Special Forces). If not for their titles, they would be "everyman" characters. This makes them easily relateable.
Second, their interactions feel very natural. This goes back to the previous point about the universe's depth. Most exposition is told through dialogue, but it rarely (if ever) feels like a character is telling you something you shouldn't already know. Sort of like when someone says "nice weather" even though the nice weather is plain for everyone to see.
Third, plot armor is very thin. I don't really want to get spoiler happy, so suffice it to say that people die and the protagonists are FAR from invulnerable. This , combined with the chronological storytelling, allows for great dramatic tension and, as Hitchcock said, tension is the key to good cinema. I should think it applies to other media as well.
So, ultimately, you have believable characters in a well-structured universe whose stories are told in an easy to understand way that also serves to create tension.