Please see link at the bottom of this post for scientific explanation of fat burning.....
I used to be a total snob about walking; I believed that if you weren't sweating and out of breath, then it wasn't exercise. I do not believe that anymore (maybe because I am older?). I am not a fan of jogging or running, but I rollerblade about 4 days a week; somewhere in between walking and running in terms of intensity - I blade 15 miles which takes about about 1 hour and 20 minutes. I also use a stationary bike about twice a week, which is a more intense aerobic workout than blading, for about 1 hour to 1 hour and 20 min, depending upon how I feel.
With no particular basis other than my gut feeling and speaking to some fitness nuts and a couple of fit doctors, about an hour of good low intensity aerobics (walking, treadmill, bike, etc.) is a good amount of time for fat burning and cardio benefits.
I do not know whether 40 minutes of walking is "better" than 20 minutes of jogging; I am not sure anybody does. Again, with no scientific basis for this, if I had to choose, I would choose the higher intensity activity that makes me sweat and breath harder; but since I do not have to choose, I do both. I like the way the higher intensity makes me feel; I also believe I get more endorphins from the intense stuff.
As we both have said, variety is key. Find a few things you like, and do them. I get bored of things easily, so I need to have choices. Personally, I prefer the more anaerobic stuff like basketball or beach volleyball, tennis; but logistically, it is really hard to do these things frequently; so I do the stuff I can do alone and schedule more easily. Do the hour long walks and hikes, and also do the 20 minute jogs, and build to 30 minute jogs and more distance.
By the way, I have found that Potassium and Magnesium have helped me tremendously with my exercise and muscle function; I strongly recommend taking them, and possibly Calcium as well.
Here is a site that addresses your question. Good luck....
http://www.fatburn.com/article_show.asp?article_id=13