If we're talking about anime adaptions of manga, I'd say I usually prefer the manga. I prefer fight scenes in animated form, and I love the soundtracks, but I think manga does a better job conveying character emotion and telling the story. When I started reading manga several years ago, I didn't think telling a story panel-to-panel would work even remotely as well, but there really are certain things that anime can't express the same way the source material can. When the author draws a scene a certain way, it's because that's how he/she means to tell the story. This doesn't always transition well into the anime, especially ones under a tight budget.
Also, when the anime is adapted from manga series, the manga canon > anime canon, so there's that. The story you're reading is the closest thing to the author's original intention. You don't have to work through pointless fillers in manga, or whatever other new additions the anime team decides to add to keep viewers entertained.
That being said, if we're comparing original anime stories to original manga stories, it makes it harder to draw direct comparisons. I suppose they both have advantages.