Eating fat gives the body no incentive to burn off from stored fat. It defeats the goal of fat loss. BUT if it makes it easier to eat less than usual, thus yielding a DEFICIT, by all means go for it.

The most important is what works for ya, not the label you use. Please remember to up your electrolytes while fasting

To my understanding the fat fast works because you are not consuming more than a tiny amount of carbs and protein...the eating of the fat is just to provide fuel and keep you from going crazy while fasting...eating the extra fat is not the reason it works, not eating the carbs/protein is the reason it works...if you are able to fast on water and eat no carbs or protein you are still getting the same benefits of the fat fast, but also not consuming any calories in the form of fat.

If you are talking about one day a week, then I expect the water fast is more efficient.

However, fat fasts can be done for up to 5 days - because you are providing your body with fuel not starving it like with a water fast. So if you want to fast for multiple days in a row, then the fat fast is a better option.

Though to be fair, if you are already fat adapted and accustomed to fasting, you might see more consistent results with 16:8 or 20:4 intermittent fasting every day vs the one day a week fast.

I have read about someone who regularly does water fasting, but that was more for histamine intolerance and it helps to improve that for a while. I would love to give fasting a go, but need to get back on track with the food first - good luck with whatever you choose to do.