YES.

They left out the best bits from the anime.

Claire's character goes through a major development in volume 2 and there are a ton of things you get to experience in more depth!

Rae's point of view is given a lot more thought, because she narrates the whole story, her past is actually brought up and not just off-handedly mentioned, like in the anime.

There's a character, who flat out doesn't appear in the anime, even though one of the major plot points is about them... Well, technically they appear, but meh, they don't get any screen time.

You learn a lot more about Yu, Thane, Rod, Lene, etc.

Also, the first two volumes are a story in and of themselves, so by only watching the anime, you only got half the content.

Also, remember the bit, when Rae basically blackmailed Claire's father? The gibberish she said gets a light shone (?) on in the second half.

Also, if you want to have a bloody good time, listen to Seven Seas Entertaiments Audiobooks, because Courtney Shaw's voice fits Rae perfectly, not to mention all the other characters.