The differences in a nut shell:

• Apple generally believes that the goal of the algorithm should be to preserve the design of the typeface as much as possible, even at the cost of a little bit of blurriness.
• Microsoft generally believes that the shape of each letter should be hammered into pixel boundaries to prevent blur and improve readability, even at the cost of not being true to the typeface.

link to the whole article (a worthwhile read for web designers)