|Actually, I think it's exactly the opposite. I think I prefer the manga to the anime. I can't explain it to you without saying a little spoiler. So here it is:
Spoiler (highlight to view)
Both of the endings are tragic, but I think the ending of the manga was a better ending for all the characters.
The anime and the manga are different. After episode 13 (I think. I'm not sure), the story is totally different. So maybe you might want to watch the anime and read the manga.