I love both the book and the movie so it was just great when my very own cousin asked for a tattoo of the red bull. (She has the unicorn too now) I will say that in the case of the last unicorn I actually like the movie better than the book. It lacks some of the story, but was put together much better. I think the writer had grown a bit from the time of the book until the creation of the movie.
One problem though is that in the movie it lets you assume the bull is bad, but doesn't really say so straight up. Considering that the bull does the bidding of another I almost wanted to take the bulls side as a kid when I first saw the movie. The only thing that stopped me was that the unicorn was so dang sweet and truth filled.