Keto Diet vs Atkins Diet for Weight Loss
Traditionally, diets are one of the go-to approaches to dealing with weight loss. American physician and cardiologist Robert Atkins popularized the use of a low-carbohydrate diet for weight loss. The Atkins Diet promoted a reduced intake of carbohydrates and emphasized protein and fat as the primary sources of dietary calories. The Atkins Diet even called for a reduction in carbohydrates from vegetables. The commercial success of the Atkins Diet led Time magazine to name the doctor of one of the most influential people in 2002, and his diet is still popular among many dieters worldwide today. 
Atkins Diet based on Carbohydrate-Insulin Hypothesis
The Atkins diet was based on the premise of the carbohydrate-insulin hypothesis of obesity. This hypothesis is couched in the belief that control of insulin is necessary for weight loss, and that by reducing carbohydrate intake, the diet could reduce post-prandial insulin fluctuation, as well as other disease states associated with obesity.
Although the diet was low-carb, it was high-protein and therefore fundamentally different from the high-fat ketogenic diet used for seizure control. Unfortunately, many amino acids can be incorporated into the glycolysis pathways and can still influence insulin secretion. This is not true for fatty acids which make up the bulk of the ketogenic diet. Consequently, the low-protein, ketogenic diet is far more likely to achieve the goals of the Atkins diet than the Atkins diet.
Atkins Diet vs Ketogenic Diet for weight loss
Weight loss with Atkins-type diets appears to be comparable to conventional hypo-caloric diets in adults (with a mean loss of 5 kg in 12 weeks).  However, studies suggest that adolescents may respond better to a very-low-calorie ketogenic diet than to a low-calorie Atkins diet (average loss of 15.4 kg over 8 weeks on the ketogenic diet vs 2.3 kg over 12 wk on a low-calorie nonketogenic Atkins diet). 
While the Atkins diet is clearly outperformed by the ketogenic diet in terms of weight loss, it may be more of a sustainable choice. The Atkins Diet actually begins with a Ketogenic Diet, which is simply called the “induction phase.” During this phase, it is recommended that you maintain your low-carbohydrate diet for the first few weeks or longer depending on personal goals. Then, dieters are encouraged to add carbohydrates slowly back into their diet, leaving the results in the hands of the individual.