Recently I started watching the One Piece anime and noticed some differences in the story line than were present in the manga, and I was wondering if there was a huge divergence in the anime over the manga like with Black Butler, or more like slight differences in plot like with Fullmetal Alchemist: Brotherhood.
The anime and manga closely resemble one another.
This is mainly because the mangaka, Eiichiro Oda actually actively participates into the animation process. So whenever they want a filler episode, they will contact Eiichiro Oda for confirmation, and he would either approve or reject it.
I believe the only deviations there were was some part in the beginning of the anime that did not totally follow the manga, and ace's tattoo. Which later on got adapted in the manga as well, so not sure how much that would count as a difference.
Well the one piece manga is the skeleton of one piece anime so there are some add ups in anime to make in more realistic and entertaining to the audience by modifying some of the portions of manga and the main difference between them is the approach of conveying the story to the readers and anime watchers .
The manga is generally a bit more viscous or bloody. This page http://onepiece.animelag.com explains what chapter connects to what episode and what arc they are in an whether it is a filler episode. Hope this helps.
The anime has lots of filler in between pages or they drag some parts out. The anime also has entire filler arcs that are not in the manga but they don't affect the overall story of one piece. I have not watched black butler or full metal alchemist so I can't compare them to one piece. I do know that it is still in the same place the manga is but just an arc behind. I know that the anime might leave false impressions in some places, for example when Luffy fought Doflamingo the anime made it look like king Kong gun had a hard time beating Doflamingo but in the manga it crushed him. Not worth to being caught up and watching one episode a week in my opinion but it is worth watching for the fights because animated fights are always better than looking at pictures.