I am sure you have read or heard that running will naturally offer greater cardiovascular benefits for the body compared to walking. This is mainly due to the required increase in workrate of the heart to sustain the more intense acivity of running. This greater intensity demands a faster blood flow - good for moving oxygen around the body. This intensity also offers numerous benefits for the heart itself and the overall strength and fitness of the body.
We have written previously about the merits of running - Is Running The Best Exercise For Fitness
A critical consideration is the additional time and effort required to participate in a run versus a walk and whether this extra effort actually causes no activity to be taken.