Certainly different from both the manga, and anime. I'd recommend this to only hardcore trinity seven fans who want to learn all they can about the characters and the story.
I suggest reading the book after everyone gets back from the floating library as this is set just afterwards and will not contain any spoilers after that point.
The translation I read was kinda rough and some parts didn't translate to English well but still a great story.
The book adds a background for the characters that don't already have one, basically what life was like before they met Arata, and is told from the trinity sevens point of view, thus you get a much deeper understanding of the characters, their emotions and what drives them.
The book also fills in some gaps in the storyline such as how arin got her spear and the breakdown phenomenon at the start of the series.
So if you're a true trinity seven fan you must read this.