If I had to choose between "Censored" and "The Gabriel Method", I would choose the Gabriel Method. I think a vegetarian (especially a Vegan) would find it almost impossible to follow BT. The reasons are:-
Research has shown that Dr Atkins was on the right track. Increasing protein (or fats) reduces the appetite - hence the three days of protein only on BT - or the two week "induction period" on Atkins.
It is not necessary to eat large amounts of fat to achieve the appetite reduction effect - lean protein will do the trick. All fats are high in calories whether they be from animal or vegetable sources. Some fats (good fats) are necessary e.g. omega 3's. Some of the good fats can be obtained from vegetable sources.
Reducing (or cutting out) carbohydrates reduces calories and cravings for sugar. All carbs are turned into sugar- which the body uses for quick energy - or to store as fat if there is a surplus. Complex carbs which take longer and use more energy to digest are better than processed carbs which turn to sugar quickly and easily.
The healthiest diet provides all the nutrients (vitamins, minerals, amino acids etc) which the body needs. If the body is lacking in any nutrients, it will try to get you to eat more in the hope that you will ingest what it needs. If the body gets calories but misses out on the correct nutrients - you will be fighting your own body - and never be able to lose weight and keep it off.
Our distant ancestors were hunter-gatherers (omnivores) - not farmers, not herdsmen, not vegetarians, not carnivores. Omnivores eat nuts, seeds, roots, berries, fruits, leaves, fish, shellfish, small animals, grubs, eggs, insects, reptiles, birds etc. Occasionally, they might get the opportunity to eat wild honey or a larger animal (not every day, and usually after expending a lot of energy in the chase). Very rarely would they eat large quantities of grains (and then only after considerable effort to harvest and make them palatable). Fruits were seasonal - and not the large sugar-loaded types we have developed in recent centuries. Foods were eaten while they were fresh.
To lose weight and keep it off (and be healthier) - eat little and often, eat a wide variety of different foods, do not exclude anything completely, do not eat anything which you can't identify unless you read the packet, restrict any "foods" which have been "invented" e.g. margarine, white flour, white sugar, sugar drinks, artificial sweeteners, colourings, flavourings, preservatives - and exercise as if you were gathering (or chasing) your next meal.
There is no one "diet" or set of rules which will suit everyone. The needs of each individual are different - and change from day-to-day. It is important for each individual to find a long-term lifestyle which suits them and their nutritional needs. It is not just about calories and exercise. Achieving a BALANCE where your body is not deprived is the difficult part.
The Gabriel Method re-educates the body and mind to a healthier lifestyle. It does not forbid anything. You don't have to weigh, count, or measure. You don't have to buy anything except the book and fresh food. You just have to give the body the nutrients it needs first - before you eat anything else.