What's Best for Weight Loss: Cardio or WEIGHT Training?

Your program should consist of a combination of resistance exercise (weight training) and cardiovascular exercise (aerobic). One or the other won't usually be enough for long term fat loss.  

As stated above, the body likes to burn muscle before it burns fat. Weight training forces your body to conserve and build muscle, thus preserving it.  If you weight train, your body wills not burn muscle tissue for energy!  Now your body just has 2 things to burn:  glycogen and fat.  How do we get the body to burn the fat? Aerobic exercise!  This consists of any low to moderate intensity, long duration activity. Cycling, jogging, rowing, dancing, stepping (stair climbing) are all aerobic activities. These primarily burn fat, after the glycogen is used up.

How do we use the glycogen up? This is where the weight training comes in. The trick is to do your weight (anaerobic) workout first, which burns most or all of your glycogen and then do your aerobic exercise! The body then has nothing left to burn but fat (remember, it won't burn the muscles because it needs them for the weight training). 
You can still burn fat from cardio without weight training first, but it takes the first 15-20 minutes to burn off the glycogen before it even starts to burn fat. This glycogen is put to better use to power a weight session and cuts the duration of your cardio by 20 minutes. Since you're weight training anyway it makes sense to add just 15-20 minutes of aerobic exercise after your workout.

To put it simply: Do an intense weight workout for about 45 minutes and proceed immediately to your aerobic activity (cycling, Stairmaster etc.) for at least 20 minutes.  This will supercharge your body and keep it in the "fat burning mode" for several hours after (your body can't easily store fat while it's burning fat). You can sip a carbohydrate drink as you do the aerobics, and have a high protein meal or shake within one hour of completion.  Be sure to drink lots of water throughout. I suggest workout 3 times per week for fast benefits.