I'm late to this thread lol but I'll also say the manga. There are multiple drawbacks to the anime, & I'll specifically highlight 3 of them:
1) Fillers (duh). Bleach anime is ~45% filler & you'll be constantly checking a filler list unless you actually want to watch them.
2) The anime got cancelled, and thus couldn't complete the story. The Thousand Year Blood War arc is hit-or-miss so certain people might not consider inclusion of the final arc an asset.
3) The anime does a poor job with exposition, cramming about 75 chapters of content in the human realm into the first 20 episodes. It's evident that Studio Pierrot wanted to rush to the rescue mission.
Of course the anime does hold some things over the manga, like the consistently good animation and my favorite OST in anime. I just don't think this outweighs the pitfalls.