Reviewing both volumes here.
I saw the Princess Tutu anime a few years back, and completely loved it. The manga, however, is a very different thing. From what's in the manga, it looks like they were developed at the same time from a basic plot outline (a girl turns into Princess Tutu to help her mysterious schoolmate, Mytho, recover pieces of his heart) and allowed to develop entirely seperately.
So what's the difference? The storyline in the anime ended up being longer, more complex, and in tone far more of a fairy tale with some interesting metafictional elements. The manga is a very straightforward magical girl series with ballet as the gimmick. And as that, it's pretty good. It just doesn't really compare to the anime. I greatly prefer the anime, but I did enjoy the manga, too. I feel like it could have used some more time to fully explore the elements that it introduced (the anime does this far better, even in the identical elements). It also lacks the bittersweet ending of the anime, in favor of a far more conventional, if open, ending.