There was a study on this. Any diet (WW, SW, LCHF) worked as long as you stuck to them. The low carb diets were more easy to stick to short term (presumably because the combination of fat and protein reduces hunger) but all of them resulted in a similar weight loss over a certain time period.
The issues occurred once the "diet" period stopped. Everyone went back to their pre diet way of eating and everyone regained the weight.
It isn't as simple as "eat less move more" because while a calorie is a calorie regardless of what it comes from, some food types are associated with insulin spikes and drops (with resultant cravings) while others have a lower GI, others make you feel fuller for fewer calories (the LCHF diet wins there). However in the main, all diets aim to reduce your calorie intake.
Losing weight is about 80% dietary intake and 20% exercise. However, exercise tones up the skin and muscles and makes you feel better about yourself, produces endorphins to make you feel good (and want to do it again), and does burn up a few calories so it's easier to maintain a calorie deficit.
There is also a lot of stuff coming out about biomes, probiotics, the varying populations of gut bacteria and their effects on mental health and body size - all of which I expect we will see more of over the next few years.
The best way to lose weight and keep it off as far as the studies go is to realise it's a long term lifestyle change and not a quick fix. Quick very low cal diets are great to kickstart weight loss if you want some motivation (slimfast etc) but for sustained weight loss you need easy to maintain small changes, new habits.
As little as two biscuits with your morning cup of tea that you don't really need can put on over 5kg in a year. Stop them and you'll lose it again.
It costs around $1000 (according to the last lecture I went to) per year to buy the food to maintain every additional kilo that you are overweight. So for someone who is 15kg overweight, they are spending $15000 extra on food every year to maintain that weight level.
The other mindset change needed is to realise that feeling hungry isn't a bad thing. It's just a sensation. You don't need to eat the moment you feel slightly peckish - have a glass of water and you may not be hungry 15 minutes later.