There are two main differences that manifest themselves throughout the entire curriculum.
1) Montessori believes that children are firmly rooted in reality, and Waldorf believes that children are part angel who don't fully "come to earth" until they lose their baby teeth at age 7. Many Montessori activities (which are called "work," much to the chagrin of people who think that this makes it sound dreary and dull) are having the child do real-life activities, such as pouring water, bathing dolls, scrubbing potatoes, sweeping, washing hands, tying laces, etc. Montessori believes that the child derives the most satisfaction from copying grown-up tasks, and gives children opportunities to do these sorts of tasks using specifically designed, child-sized tools. Montessori has nothing against fantasy or make-believe, there is just the idea that during the 3 hours a day that kids are in preschool, they prefer to do useful things. Waldorf uses many of these same sorts of real-life tools and activities (mini brooms, lots of cooking), but that's supposed to be firmly ensconced in a very German sort of kinder kuche kirche lifestyle.
2) Montessori believes that all children develop at their own rate, and that if you give children access to a range of developmental tools, plus a teacher who is trained to gauge where the child is at and when they're ready to move forward, they will grow in leaps and bounds when they're ready. Waldorf believes that all children develop at a very lock-step pace, based on their age. Steiner believed that until a certain age, children aren't ready to know anything about the real world (until they're 7 you're supposed to tell them that weather fairies cause rain), reading or other academic pursuits, or even use certain color crayons. If you google for information about anthroposophy and child development you can find more information.
I was really into Waldorf before I looked deeply into it and found out what it's all about. Now my daughter's at a Montessori preschool.