There's little question that running burns more calories per hour compared to walking. However, the debate has stood whether or not you burn the same number of calories running vs walking the same distance. Studies show that running does, in fact, burn more calories per mile. This can be accounted for by the extra work your body does to spring from one foot to another and the increased amount of oxygen you consume per minute while running, which burns more calories in a shorter period of time. Find a link to the analysis in the References section.
Both running and walking engage the muscle groups in your legs and provide a lower body workout. Just as it takes more calories to run, it also takes more muscle. Because your knees spend more time bent, or flexed, during a run, your knee flexors, or quadriceps, work significantly harder while running. Although other muscles, such as your hips, also work more during a run, the primary increase in muscle use is found in your quads.
Contrary to the common belief that chronic joint problems arise from the high impact of running, studies suggest otherwise. A study by Stanford University followed distance runners over 20 years and found that they had healthier knees than their non-running counterparts. Researchers concluded that, over time, running may condition joints to high impacts, which may help reduce the degeneration of cartilage.
A study published in the Clinical Journal of Sports Medicine found that runners were more likely to suffer from sports injuries than walkers. While walkers may have chronic injuries like shin splints and plantar fasciitis, runners are more likely to suffer from acute injuries, including sprains, strains and even fractures.
It's important to consult a physician before you start any workout program. Because of the higher impact, running may cause joint pain for someone who is obese. Similarly, if you have a history of joint problems, the lower impact of walking will be gentler on your body. Running may help to preserve healthy joint cartilage, but may aggravate joints that are already compromised.