Basically, both value a child's independence, creativity and the child's needs. Personally, I've heard that the Waldorf has some aversion towards technology while the Montessori treat computers as a way to provide access to information but will not be controlled by it.
Most of us are more familiar with the Montessori system and if I had to pick one, I'd pick the Montessori.
To read more about similarities and differences between the two, you can read the following:
http://www.michaelolaf.net/MONTESSORI%20and%20WALDORF.html