Well I'm not in the best fitness state yet and as a result I cannot maintain a jog for that long.

My best so far has been to jog continuously for 20 minutes at 5mph.

Walking wise, well, I can try and do what I can to be honest. For a fair while I was going for walks as good as 4 miles over 450 vertical yards.. this over 60 minutes burns around 800 calories.

Jogging as mentioned above only manages to burn 200-300 calories but the exercise results in the higher heart rate.

Given that I am trying to lose weight/body fat, which is the ideal thing to do here? The walking or the jogging?

Combining it would be an easy solution, but because I lack fitness I can't keep up the interval work that well and if I get too puffed/tired I don't have time to stop and catch my breath or anything (when on a treadmill.)

What should I be doing here?

This is an easy answer, well for me actually. People who are just starting to jog shouldn't delve right into it, you have to learn to crawl before you can walk

Simply if you wish to walk but would rather be able to jog to burn more calories, you should power walk. Power walking is walking at a heightened speed so that your heart rate changes. Although with power walking, you are walking, but it is similar to a midway between jogging and walking. It is also a fairly good exercise and quite better than just simply walking. I suggest you give it a try.

Well done on jogging for 20 minutes! I remember I could only jog for abuot 5 minutes at a time and now I can run for 50 minutes!

The only thing im wondering about is how walking 4 miles burns 800 calories? Over the same distance, jogging and walking burn about the same amount of calories. Jogging just takes about half the time.

So for weight loss... whatever works best for you! Maybe focus on distance, not how you get there?

It's over 500 vertical metres though, so in other words, 4 miles up a rather large hill.. treadmill is on an average of around 8.5% incline

Hi Nixon, you are on the right track....read on:

Secret #1 – Do not engage in moderate exercise. Your appetite will increase immediately after your exercise. You are not burning much fat, but burning your carbohydrates mostly. You are also building up muscles and muscles are 22% heavier.

Secret #2 – Do not engage in vigorous exercise. Your appetite will decrease immediately after, but will increase the next 3-5 days. You are burning 0% fat, and burning 100% carbohydrates!

Secret #3 – To burn those fats quickly, you should do light activity like walking, household chores, grocery shopping, carrying an infant, or even walking up stairs. Though light activity, you will lose 30-60% fat. Not bad!

Such terrible advise and poor understanding of even simple exercise physiology.