It's actually true that walking and running for equal distance will burn equal amounts of fat. When you're walking (as in exercise, not strolling or window shopping), you don't need fast energy and the body preferentially burns fat. When you run, the body uses more sugar and less fat. The net result on fat loss is nearly identical.
However, running is much better for cardio than walking is. That's a given. It just depends on how much stress you are willing to put on your knees and hips. If you're still quite heavy, you're better off doing low impact work like biking, elliptical, swimming, rowing, walking lunges so you can spare your joints. Joint pain is no fun.
1) eat real food - more vegetables, moderate meat, moderate fruits, less grains, less sugar, less vegetable oils.
2) exercise - moderate intensity cardio, sprinting, heavy lifting, dedicated stretching and mobility.
3) live - relax, de-stress, meditate.
Disclaimer: I'm not professionally qualified to make any formal recommendations. I've just done my homework and I'm my own guinea pig. All of my data, unless otherwise cited, comes from a sample size of n=1 (me).