If a long time walker, am I healthier than if I run?

Not necessarily. Aerobic exercise has been shown to be beneficial. Running is a more strenuous aerobic exercise. However, you may not be fit enough to tolerate the stresses of running. It is best to focus on getting at least 20 minutes of aerobic exercise several times a week. Any kind of aerobic exercise that gets and keeps the heart rate elevated (generally above 120 bpm) is good.
Walking is a Winner! Walking provides all the desirable benefits of aerobic exercise. Muscles are utilized, endurance improves and cardiorespiratory health is definitely promoted. Running is a wonderful activity as well, but allows for increased compressive and shear loads to be transmitted through your joints, which is fine unless one already has joint problems such as pain, swelling and/or arthritis.