Note: This explanation does not concern itself with body health, wellbeing, the ability to follow/sustain the diet short/long term, impact to nervous system or the psychological impact of satiety that low-carb diets can offer. It only concerns itself with the imaginary scenario of two identical subjects following the same total calorie diet but with macro-nutritional differences.
Are Carbohydrates fattening?
The question asks if carbohydrates lead to more fatty mass gain than the other macronutrients: fat and protein (and alchohol), if consumed at the same calorie level.
To put it another way: For weight change, does the macro-nutritional profile of a diet affect the rate and total amount of fat mass gained?
The common tautology employed by people proving that macro-nutritional profile is not important when it comes to weight loss is "a calorie is a calorie".
Evidence For, or "A calorie is a calorie"
Several metabolic ward studies have shown that there is no difference in weight loss when protein intake was held constant. If you're really looking for a metabolic advantage through manipulating macronutrient, you'd be far better off putting your money on protein. There's actually some evidence that higher intake levels do convey a small metabolic advantage.
Unsurprisingly, the studies into macronutrient impact on mass change are numerous but by no means perfect. One has to cast a very critical eye over all the conflicting evidence (and mud-slinging) and make their own decision.
A good meta analysis of the above tautology by the well-respected Buchholz AC & Schoeller DA. concluded that:
...Neither macronutrient-specific differences in the availability of dietary energy nor changes in energy expenditure could explain these differences in weight loss. Thermodynamics dictate that a calorie is a calorie regardless of the macronutrient composition of the diet...
Buchholz AC, Schoeller DA. Is a calorie a calorie?. Am J Clin Nutr. 2004;79(5):899S-906S.
This referenced a ward study (amongst others which also concluded the same):
Both the high-carbohydrate and high-protein groups lost weight (-2.2+/-0.9 kg, -2.5+/-1.6 kg, respectively, P <.05) and the difference between the groups was not significant (P =.9).
Sargrad KR, Homko C, Mozzoli M, Boden G. Effect of high protein vs high carbohydrate intake on insulin sensitivity, body weight, hemoglobin A1c, and blood pressure in patients with type 2 diabetes mellitus. J Am Diet Assoc. 2005;105(4):573-80.
To continue the evidence-train for there being no win in carbs-vs-fat:
In a 2003 study by Bravata DM, et al. the conclusion was that nutritional-profile really doesn't affect total weight change at a significant level.
There is insufficient evidence to make recommendations for or against the use of low-carbohydrate diets. [...] Among the published studies, participant weight loss while using low-carbohydrate diets was principally associated with decreased caloric intake and increased diet duration but not with reduced carbohydrate content.
Bravata DM, Sanders L, Huang J, et al. Efficacy and safety of low-carbohydrate diets: a systematic review. JAMA. 2003;289(14):1837-50.
A 2009 study directly comparing the weight loss "fad" diets concluded that provided you reduce calories, the method you do this is not of importance:
Reduced-calorie diets result in clinically meaningful weight loss regardless of which macronutrients they emphasize.
Sacks FM, Bray GA, Carey VJ, et al. Comparison of weight-loss diets with different compositions of fat, protein, and carbohydrates. N Engl J Med. 2009;360(9):859-73.
A 1996 study also concluded the same thing:
The results of this study showed that it was energy intake, not nutrient composition, that determined weight loss in response to low-energy diets over a short time period.
Golay A, Allaz AF, Morel Y, De tonnac N, Tankova S, Reaven G. Similar weight loss with low- or high-carbohydrate diets. Am J Clin Nutr. 1996;63(2):174-8.
An Australian study put them head-to-head over 12 months and didn't find a large difference:
Under planned isoenergetic conditions, as expected, both dietary patterns resulted in similar weight loss and changes in body composition. The LC [low carbohydrate] diet may offer clinical benefits to obese persons with insulin resistance. However, the increase in LDL cholesterol with the LC diet suggests that this measure should be monitored.
Brinkworth GD, Noakes M, Buckley JD, Keogh JB, Clifton PM. Long-term effects of a very-low-carbohydrate weight loss diet compared with an isocaloric low-fat diet after 12 mo. Am J Clin Nutr. 2009;90(1):23-32.
A 2010 study went a step further and did a 2-year study across over 300 participants; patients lost an average of 7 kg or 7% of body weight, and no differences between the 2 groups were found:
Successful weight loss can be achieved with either a low-fat or low-carbohydrate diet when coupled with behavioural treatment.
Foster GD, Wyatt HR, Hill JO, et al. Weight and metabolic outcomes after 2 years on a low-carbohydrate versus low-fat diet: a randomized trial. Ann Intern Med. 2010;153(3):147-57.
Taking a different view and looking at weight gain, there are fewer studies but the evidence points to the same outcome.
There was no significant difference in fat balance during controlled overfeeding with fat, fructose, glucose, or sucrose.
Mcdevitt RM, Poppitt SD, Murgatroyd PR, Prentice AM. Macronutrient disposal during controlled overfeeding with glucose, fructose, sucrose, or fat in lean and obese women. Am J Clin Nutr. 2000;72(2):369-77.
This can be also seen in this small 2000 study:
...fat storage during overfeeding of isoenergetic amounts of diets rich in carbohydrate or in fat was not significantly different, and carbohydrates seemed to be converted to fat by both hepatic and extrahepatic lipogenesis
Lammert O, Grunnet N, Faber P, et al. Effects of isoenergetic overfeeding of either carbohydrate or fat in young men. Br J Nutr. 2000;84(2):233-45.
A important point to note is that dietary fat is what is stored as bodily fat, when a caloric excess is consumed. For dietary carbohydrate to be stored as fat then they must undergo a conversion through 'de novo lipogenesis' which will occur when the carbohydrate portion of someone's diet alone must approach or exceed ones total daily energy expenditure (TDEE). You can read more here
In addition, for a comprehensive primer on insulin and how it functions please check out this post on weightology which is summarised in layman on reddit by /u/ryeguy, here.
Evidence Against, or "A calorie is not just a calorie"
I cannot find evidence to support the opposite viewpoint. However there is criticism of the studies done these are found in the "Dear Sir"'s in the ASfCN/
A post by Anssi H Manninen is critical of a Bravata study:
Bravata DM, Sanders L, Huang J. Efficacy and safety of low-carbohydrate diets: a systematic review. JAMA 2003;289:1837-50.
She states that:
...In the true low-carbohydrate group, the mean weight loss in trials was 17 kg, whereas in the higher-carbohydrate group it was only 2 kg. Oddly, the authors did not consider this significant. Only by intermingling the results of trials of low- to medium- and high-carbohydrate diets could the authors have reached the misleading conclusion quoted above.
In another article Richard Feinman and Eugene Fine dispute the assertation of "a calorie is a calorie" using the first law of thermodynamics by stating that the second law must also be taken into account.
What should I eat for weight loss?
Eat less. Different diets can make this easier, so pick whichever one
best fits your lifestyle. Ultimately, you need to reduce your caloric
Many diets, fad or not, do work. This is mainly because they reduce calories.