Yes it is possible to lose more weight on juice than water. But it is not which one is better but your body decides where it should place that extra energy from not digesting food. You should enjoy reading this webpage about the rate at which someone loses weight. It teaches you to trust your body's intelligence. Plus stress is fattening so do not worry about how fast you lose weight.
I would not recommend fasting to lose weight. There are much safer alternatives and all it takes is determination. Take your drive and focus from the liquid diet and eat healthy meals with smaller portions. The possibly get your heart rate up to a fat burning level for about 45 minutes and you already set your self up to lose weight really fast, but in a safe way