From what you've written about the TV series it seems like it was adapted pretty well, the books definitely makes you both laugh and cry at times as well.

The biggest difference (I think? Again, as i havent watched it yet and only have what you've wrtten to go by) the TV series mostly focuses on Rasmus and Benjamin, the books also talk quite a bit about the friend group they make through Paul, but I imagine they had to pick a main focus when adapting it.