– The story is ahead of the anime and you don’t have to wait as long for an update.
– In some cases the manga has a complete story where as the anime counterpart can get cancelled for numerous reasons.
This.
I’ve said this in other threads where the topic comes up, but I’ll generally go to a manga after I’ve watched an anime. If the anime was good and there seems to be no chance of it getting more episodes, I’ll go to the manga to continue the story. If a manga ends well enough, and they actually decide to finish the anime down the road, I check it out usually. I did a full rewatch Naruto. I’ll watch the final Bleach Arc. I’ll go back to One Piece, probably. Maybe one day I’ll watch the final season of Fairy Tail, but considering 100 Year’s Quest is going on, that isn’t likely, because that counts as the story not being finished for me.
If I had a choice, though, I’d always watch anime first because I do enjoy the stories actually moving, ie. fight scenes are always better animated.