I agree with JCW - while running does burn slightly more calories per mile than walkin (because you are actually airborne for part of each stride), it is distance that is the major factor.
There are health and fitness benefits however in getting your heart rate higher.
However, the impact of running can be hard on the legs, and it takes a while for your leg muscles and tendons to adapt. The best way into running is through a Couch to 5K program, which basically mixes in progressively increasing intervals of running and walking over several weeks. www.sparkpeople.com/resource/fitness_artic