You can't get more cost efficient than walking and running. Both are stellar options for aerobic exercise. If you're like me, you have a definite preference between the two (I HATE running). But if you're on the fence about which to do, her's some things to consider.
I think its safe to use real life experience to figure out which activity is more intense. Running causes more huffing and puffing. You might want to do something intense for a short amount of time, making running the better option. If you don't want to tire yourself out or are just getting into exercise, you might want to walk.
Burning fat wise, which, let's be real, is the main reason we workout, running definitely comes in first. Running is much more intense meaning calories are burnt more efficiently. You'll burn more calories both time and distance wise. Contrary to popular belief running a mile burns more calories than walking a mile. Plus when going at a faster speed, you'll be able to log in more miles anyways.
Table A: Calories Burned Per 1-Mile Walk* vs 1-Mile Run** For A 156-lb Subject
* one mile walk in 18:36
** one mile run in 10:00
Running is a high impact activity, whereas walking is a low impact. Walking always leaves one foot on the ground, whereas running gives a brief second where you're completely in midair. For your joints and injuries sake, low impact is better, making walking the better choice.
Looking to limit your calorie intake? Running actually regulates appetite hormones. Running may produce the hormone peptide YY, which can help with appetite suppression.