This is a tough question to answer as there are a lot of ifs and buts.
Weight loss is all about caloric deficit, expend more energy than you consume and you lose weight. Most people do this by dieting, but the body tends to readjust the resting metabolic rate so that you don't lose too much reserves. Thus exercise plus diet is needed for weight loss to be effective.
How effective is 'Diet Only' versus 'Diet plus Exercise' for Weight
Loss? Most studies demonstrate that when diet (caloric restriction)
and physical activity are combined in a weight management program,
encouraging results in weight loss occur. Donnelly and colleagues
(2009) explain that a weight loss program design may create an energy
deficit (e.g., 500 to 1500) composed of exercise (e.g., 250
kilocalories/day) and caloric restriction (e.g., 250 kilocalories/day)
for the daily caloric deficit total (500 kilocalories in this
example). In studies where investigators introduce an energy deficit
of 700 to 1000 kilocalories per day, 'diet only' and 'diet plus
exercise' result in similar losses. Donnelly explains that this is due
to metabolic adaptations that “diminish any additive effect of energy
expenditure from physical activity on weight loss”. However, in
investigations where the energy deficit is 500-700 kilocalories/day,
the 'diet plus exercise' group is about 20% greater than the 'diet
only' intervention.
So weight loss needs to be related to your activity and diet in order to understand your basal metabolism. But weight loss isn't just about bodyweight as it is about losing bodyfat (as muscle is useful for maintaining basal metabolism and body function). When you calculate this you are able to figure out how many calories need to be removed from the diet in order to lose fat. See here. There are also strategies that can change your metabolism.
Exercise is usually broken down into two categories: cardio and weight training. There are many benefits to both and generally both are recommended for long term health. Weight training is known to burn fat.
This study is the first to directly show that resistance exercise
increases adipose tissue lipolysis and thus contributes to improved
body composition. This boost in lipolysis is apparently due to the
excitatory effect of resistance training on specific hormones (e.g.,
epinephrine, norepinephrine and growth hormone). As this study design
was completed with trained male subjects, it is hoped that the methods
and procedures will be completed with other subject populations (e.g.,
females, untrained persons, youth, seniors, overweight, etc.) in
future research.
For cardio training, there is obviously fat burning taking place. The amount of fat burning that occurs is related to the intensity of the cardio.
In summary, that data clearly show that exercise intensity is the main
factor in determining the magnitude and duration of EPOC following
aerobic exercise. Thus, when developing a cardiorespiratory exercise
prescription for weight maintenance and weight loss, the influence of
exercise intensity on EPOC and its potential contribution to total
caloric expenditure should be taken into consideration.
The same is true of weightlifting (from the same article):
The data on resistance training and EPOC suggest that EPOC is
distinctly influenced by the intensity of the resistance training
program.
The actual amount of post activity "fat burning" will be related to the intensity and duration of the exercise done. Weightlifting has advantages in terms of encouraging muscle satellite cell accumulation that sustains and grows muscle. Cardio has the benefit that it can be performed for longer durations than weightlifting. So the essential answer will come down to the individual and their strength and fitness.
Essentially any exercise program should incorporate both cardio and weight training for weight loss, especially targeting fat loss.
For more articles on fitness and metabolism see here.
