Per minute of work, running burns more calories than walking. Obviously. The faster you go the greater the difference.
But what about if you cover the same distance? If you run you will arrive sooner and burn more calories per minute. But if you walk you will burn calories for a longer period of time.
Studies seem to suggest running would still edge the overall calorie burn, but not by much, particularly if you choose to walk at a brisk pace.
Also don’t forget walking puts far less strain on your joints and connective tissues, requires less motivation to initiate, can be seamlessly incorporated into a daily routine and is much more sustainable on a regular basis.
Last but not least reducing exercise (in whatever format) to a simple energy expenditure equation is a mistake. The benefits extend far beyond burning a few extra calories!