The low carb thing works for a short period and then stops working because your metabolism adjusts to your new diet, so the weight loss stops after a couple months.
A very common complaint of low carb diets is lacking the ability to focus or concentrate, like their mind is in a fog. That's because you are starving your brain! Sugar is the brains number one source of energy. You need sugar in your diet in order to function as nature intended.
The problem with a high protein diet is that high levels of protein are actually toxic. When protein is broken down, it's by-product is actually poisonous to your system. With really high protein diets, you can have elevated levels of this toxin in your system over an extended period of time. This can cause all kinds of problems like kidney damage, liver damage, an increased risk of cancer, as well as bad breath.
The order of priority for energy sources goes like this: sugar, then protein, then fat. If there's no sugar in your diet, next in line is protein. If there's no protein in your diet, your body will actually pull protein out of your muscles before it will pull fat off your thighs. That's why anorexics look like skin and bones, they nearly literally are - their muscles have been so eaten away, you can actually see their skeletal structure. That's why you need to have adequate protein and sugar in your diet in order to lose weight without diminishing your muscles.
Another thing that's important to remember is that your liver requires fat in your diet in order to generate the hormones necessary for weight loss. Stored body fat and dietary fat are structurally different, each requiring a different metabolic process for use. So those hormones cannot be created from stored fat, it has to be dietary fat. That's why anorexics will often lose weight when they start eating normally again. On experiment done with mice found that those on a completely fat free diet did not lose weight, and ended up with excessive fat stored in their liver. The theory is that the process for breaking down the fat got halted in the liver because of the lack of proper hormones due to the lack of fat in the diet. So what fat the mice had from before the diet migrated to the liver and then got stuck there. Severe illness and permanent liver damage resulted from the fat build-up.
In order to lose weight without causing any of the above mentioned problems is to eat adequate amounts of food, and then burn more calories than you consume. And that means exercise. And since your diet won't be lacking in sugar, protein, or fat, you'll lose weight without starving your brain, destroying your muscles, or poisoning your system.
So basic point is this, you *need* fat, sugar, AND protein in your diet in adequate amounts in order to lose weight. Any diet that suggests otherwise is going to screw up your system one way or another.