In order to answer your question, it's best to review how the body's energy systems work. An article called "Death by Prowler" by Matt Reynolds has a good overview. It's an educational read, but I'll summarize a couple high points here:
- Aerobic activity burns more fat in proportion to sugars.
- Aerobic metabolism does not shut off when you push into higher demand energy systems (i.e. anaerobic activity).
Based on the Katch McCardle algorithm, resting metabolic rate is most affected by the lean mass you have. I.e. more lean mass, more calories burned at rest.
Now, the bottom line is this: you will burn more calories per given amount of time when you exercise at an anaerobic level. The major caveat is that you won't be able to keep up the anaerobic exercise as long as you can aerobic exercise. Even though the majority of the calories burned during exercise will come from blood sugars/glycogen in an anaerobic state, the body will have to free energy from your fat stores to make up the energy demands. This is what is commonly referred to as the "after burn" effect.
With aerobic exercise, your body is able to keep supplying energy at the rate it uses it. While this is sustainable, once you stop exercising, you no longer have any demand for more energy. Thus, there is no increase in resting metabolic rates.