The Anime is an almost exact rendering of the first 45 chapters of the manga. Whether you watch the anime or read the manga is mostly up to which style you prefer, although they did a splendid job with the anime. The biggest note for watching the anime is that there's a 3 episode OVA that takes place about halfway through episode 13(maybe 12?, doesn't really spoil much though in my opinion), and you just need to be careful about whether you start watching with "Those Awaiting a Star" or the anime proper.
The majority of complaints about the manga are due to what happens after where the anime ends. My personal take is that the anime ends at a really good place, just about everything came together at it's end, and there was nothing left to resolve. As such, With this new arc, Yamazaki has to rebuild all the foundations that any major conflicts for the next while will revolve around. The style however, takes a long time to do so, and as such, with 60 chapters out now, we're effectively within the first 15 chapters of the manga again (We Live and Learn). By that point all that really happened was the main cast was established, we started 1 side story, and we started into Lindel's story. That's not that bad a track for the first third of a story, but consider that chapter 21 (or even later in all honesty, I count then because that leads straight to winter, when everything goes down, but the story is still needs to introduce a character before things really take off.) is when all the dominoes have been set up, and start to topple. With the momentum completely halted by the resolution in chapter 45, it's just taking time to set itself back up.
