It can be said that the original fairy tale and the Disney movie are very different from each other. The first major difference is the status of Belle and her family. In the original tale, her father was a wealthy salesman and she had two sisters. In the Disney film, she is the only child, and she and her father don't appear to be wealthy.
The first encounter with the Beast is also totally different. For starters, the presence of living objects in the castle was not in the original story, and was entirely invented for the needs of the Disney film.
The Beast also has a very different character from the fairy tale. In the Disney version, he typically angry, but still whimsical and good-hearted. On the contrary in the fairy tale, the Beast is not at all choleric. He is kind, considerate, tender, and would do anything to fulfill Belle's desires.
The rose plays a more important role in the Disney version. In that version, it was given to the Prince as a present from the enchantress in exchange for shelter from the cold. After refusing, the Prince is turned into a Beast, and must find true love before all the petals, or he'll be cursed forever. In the fairy tale, the rose was a present that Belle asks her father to bring to her. This is stolen from the Beast, pushing him to demand one of the father's daughters as a sacrifice.
Many of the characters of the Disney version are not present in the fairy tale. In the original, the only noteworthy characters are Belle, the Beast, Belle's father, the two sisters, and the enchantress.
There are however a few story elements that both versions have in common. The parts where the Beast transforms, and where the Beast offers Belle his great library are present in both versions.
It's easy to point out that the two versions are vastly different, but each one has its own charm. Perhaps you will have a preference, maybe not, but it's always interesting to compare the two.