I don't have a whole lot of series in both manga and anime versions, but of those I do have I think the manga of Video Girl Ai and Please Save My Earth are far better than the anime versions. Mostly this is because the anime series are far too short, the VGA anime doesn't do too bad a job as it only covers the first few chapters and ends the story at a convenient point while the PSME manga doesn't split into separate stories so neatly and the story is way too long and complex to be done coherently in less than 24 episodes.
On the other hand there is one series where I have both anime and manga where I think the anime is far better than the manga, and that series is Magic Knight Rayearth where the anime of the second series especially is far better and makes more sense than the manga version.