@hisholykingdom
it is what your body naturally wants to do and was designed to do.
When needed. Walking is our primary function with running as a second on an as needed basis, primarily for getting away from threats. In that regard, sprinting is more appropriate rather than long distance running.
Here's a study from 2013. Now overall it does seem to suggest an increased benefit for running, over time, however the only downside is that there were limited controls as the subjects were self reporting and not held to particular intensity standards. But as a snapshot of the average population...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4067492/
These results from these very large, prospective, cohorts suggest that equivalent doses of running (a vigorous exercise) and walking (a moderate exercise) are associated with equivalent reductions in the risks for new onset hypertension, hypercholesterolemia, and diabetes.
Furthermore, it does not appear to matter whether these exercise doses are achieved by running or by walking.
Now, it does say
The runners’ results showing increased benefit with increased running energy expenditure also provide confirmation in a new independent sample of a progressively beneficial dose-response relationship for this activity
Basically, running, you're burning more energy. More energy means lower BMI which means carrying less baggage around putting strain on your frame. That's the basis for most of the benefits, get rid of the baggage. BUT, there's also an increase risk for injuries such as runner's knee, achilles tendonitis, shin splints, plantar fascitis, stress fractures, etc. Once you incur one of these injuries, you're not going to be running AT ALL for a while preventing you from obtaining ANY benefit.
Walking is lower impact and less risk for injuries meaning that over time you can get more benefit out of it with less risk. Of course the best exercise is THE ONE YOU'RE GOING TO DO and the one that you'll do CONSISTENTLY. Absolutely, go back and forth between walking and a light jog, a sprint, or whatever feels right.
If you can afford it or have access to one, an elliptical machine is great because you can get the intensity much higher than walking while removing all concerns over impact of running. I keep one in my office at home so I can jump on it anytime I feel the need.