If you look to research, you can easily find a study to support whatever you want to believe.
One example is a study Dr. George Blackburn, 
associate director of the Division of Nutrition at Harvard Medical School who concluded that diet or nutrition is by far the greatest predictor of weight loss success. He suggests that an extraordinary amount of exercise is required to get reasonable weight loss.
Another study led by Judy Cameron, PhD, senior scientist at Oregon National Primate Research Centre and Professor of Behavioural Neuroscience and Obstetrics/Gynaecology at Oregon Health Science University showed that “Far and away the biggest predictor of weight gain is how active we are – that overrides how much food we are eating”. The study may explain why people who try to lose weight by dieting alone rarely succeed.
Dr Timothy Church from the Pennington Biomedical Research Centre of Louisiana State University conducted a study that suggested the problem with exercise for weight loss is a problem called “compensation”, i.e. those who exercised cancelled out the calories they had burned by eating more, generally as a form of self-reward. He did however go on to say that even if exercise doesn’t help much in the battle to lose weight, it is essential to maintain weight loss.
Whatever the case, we routinely underestimate the amount of food we eat & overestimate the amount of exercise we do.
Also, we often sabotage our efforts to lose 
weight by unnecessary eating. As an example, 1 x 100 gram slice of chocolate cake will take 34 minutes of running at 10 kph to burn off. Therefore if you are going to eat this or something similar after exercise you are wasting your time or on the other hand, if you eat the cake and then exercise to burn it off; you may as well not have eaten the cake; that would be easier.
But what will really work for you?
You can take weight off through a whole variety of strategies. What most studies seem to agree on however is that most people don’t keep the weight off unless they are physically active.
There are 7700 calories (32,340 kilojoules) in 1 kilogram of fat. So if you expend 7700 calories in exercise (let’s sat over a 7 day period), you will lose 1 kg of weight or if you reduce your calorie intake by 7700 calories over that same 7 day period you will also lose 1 kg in body fat. I think the key comes down to the individual. What are you most likely to be able to maintain. For most it is a combination of both exercise and calorie reduction.