During calorie restriction while eating a normal diet, especially one with a high glycemic response, the intensity of hunger will reach levels that may be intolerable. Staying in keto will keep your body on fat burning mode, and your hunger pangs will be less even if you are consuming less calories than you are using.
The transition from using glucose as energy source, to using fat as energy source, creates a strong hunger response. Hunger is also affected by the hormones ghrelin and leptin. These vary by time of day, and I think are related to the circadian rhythm. So it may also help to eat on a schedule.
Note: The use of your own fat for fuel can reduce growth hormone levels, as the body switches from feast to famine mode. Although there seem to be workarounds, because growth hormone secretion happens at specific times.
One research paper found a link between a high fat diet and adipocyte apoptosis (fat cell death).
I have tried a meat and non-sweet-vegetable only diet (high-protein), for 6 weeks, and I was always in a state of hunger no matter how much I ate, but I think that this only applies to my own body type. Or, it only applies to a body and mind with a life long history of a high sugar and starch diet. Your experience could be completely different. Regardless of choosing a high protein, or high fat diet, I think most people would benefit from reducing the amount of carbohydrates, especially, simple sugars. Edit: I found out the body can convert protein into glucose, and so maybe, I was always transitioning in and out of ketosis. Likely, the transition in and out of ketosis was causing periods of elevated hunger.
Diets to lose weight in the short term may not be the solution: Diets Are Not the Answer. Lifestyle changes in what you eat, will lead to sustained weight loss, and better health. It's up to you to experiment, and find out what works best for your own energy processing engine.