The Manga is definetely more on the point and doesn't drag things out to much.
The anime suffers from the same syndrome most long running anime based on mangas does, some-times, it ends up dragging things out far more than it should have, to try and buy some time so it wont catch up with the manga.
But on the same time, some of the things it does add is very very appreciative and leaves more room for the characters to breath and be themselves, some of the things the anime adds does indeed feel like it lacks in the manga, and it brings some very emotional moments where music, animation and it all just comes together.
It's a give or take, you can definetely go ahead and read the manga first, then find out what the anime added and have some fun with that.