The main advantage walking has over running is that it's low-impact; so there's less wear and tear on your cartilage and bones. This also opens walking to many who might not be physically able to run, like the elderly or the very overweight.

If your primary goal is weight loss; then running, perhaps not surprisingly, is going to provide more dramatic results. But look at the results of our own independent study:
A walker who walks one mile a day will burn 100% more fat than a runner who runs zero miles a day.
Ok, admittedly, our study wasn't peer reviewed or very rigorous. But the point is this: because it's a smaller commitment in terms of sweat, many people may be more likely to stick with a walking routine than running. So how many calories are burned in running vs. walking? According to this chart published on the Mayo Clinic website, an hour of running burns more than twice as many calories as an hour of walking. So, if your decision to begin walking now leads to running further down the road, great! The important thing is to get started. And walking is something you can do right now -- literally -- just get up and go walk.