You can argue till you are red in the face about which one is better, and true some are better than others, but the bottom line is you need a caloric deficit in order to loose weight.
The best solution is to eat a balanced diet, follow a sensible exercise routine, more importantly, stick to it. That is called “lifestyle”. You need to adopt a good “lifestyle.”
You can eat anything and still loose weight, you can eat only animal protein or fat or both, without carbohydrates and still grow fat.
Also, the Atkins and the keto and the high carb, etc. are the way your body works. It just works a little different with each one. Your body is “designed” (now do not start saying that I am a creationist because of the choice of words) to:
Change excess calories not consumed into fat, to use at a latter date, when food is low and you need the reserves.
To use stored fats when your food intake is lower that your caloric expenditure, for whatever reason.
To change sugars and carbohydrates into glycogen and sugars that your body can use directly for the generation of energy, ,and store the excess as fat.
Use protein, mainly animal but vegetal as well, to create muscle.
Use vitamins and minerals to regulate and help in the functioning of your body.
Today’s regular diet is heavy in sugars and carbohydrates at, which are not bad and are necessary. The amount is the problem. Simple and processed carbohydrates are easily converted in glucose, which in turn increase your blood sugar (too high = hyperglycemia), resulting in an increase in the production of insulin to lower the sugar in your blood (too low = hypoglycemia). Now the high intake of simple carbohydrates result in hyperglycemia which shoots up insulin production causing hypoglycemia). That is why today’s regular diet is bad, you become a yoyo, with glucose level going up and down constantly, and creating a sugar dependency which takes you to insulin production and use problems, Diabetes Type 2.
Now, throw sedentarism into the mix and everything becomes deadly. Obesity, Diabetes Type 2, cardiovascular problems, sleep disorders, etc.
Want live long, just lower your simple carbohydrate intake, flour and derivatives, and sugars and related foodstuffs, complex carbohydrates are less problematic since they do not shoot up your blood sugar, which keeps the insulin under control. Control your fat intake to moderate, but only good fats; and control your protein intake (amount, although type is also important).
More importantly, increase your exercise, if you do too little or none. And above all lower your overall caloric intake to a lower level than your caloric consumption until you reach a sensible weight for your age and body type. Then keep a balance diet with frequent exercise and that will keep you healthy.
Remember, it is not the fat, the proteins, the carbohydrates, it is the amount of calories.