This is coming from someone who has both watched the anime and read the manga: you won't be missing up much if anything by watching the anime for the 1st part, before the TS. Rather, it even improves some sad scenes with powerful and over the top theme songs and voice acting, I won't name them because it's spoiler.
But as for after the TS, then yeah, you are better off changing to the manga. You can still watch the Sabaody part 2 in the anime since some moment there is made more epic in the anime, but after that, switch to the manga.