Agreeing with Cerain, the light novel is definitely more detailed. There are 23 chapters out right now, and it only caught up to the end of chapter two around chapter 20. This is partially because the chapters are kind of short, but also because we get more information. For example, her brothers and the capture targets, including the prince, were kind of stalking her. They literally watched her read books for ten hours, then stalked after her to see her practicing her sword at night in secret. I'm just going to assume the manga isn't gonna let us know that, since it already happened, so it's not a spoiler.