It depends on the series for me. Some manga series can't be beaten by their anime counterparts, whereas other series are handled well in anime-form.
For example, Alien Nine. Nice manga, sure. In fact, the manga explains a lot. However, the anime (especially the end) is far better than what the manga did simply because it was so loose that it could be interpreted so many different ways. (That and Yuri, Kumi, and Kasumi's anime forms are all a bit more adorable than their manga forms.)
On the other hand, I personally think that Samurai Deeper Kyo as a manga didn't make the series look like a cross between Bishoujo Senshi Sailormoon and Rurouni Kenshin. So, a fan can really take the manga more seriously than the anime, which is, in my opinion, a good thing (as SDK does have some serious points that are just lost in the anime).