Disclaimer : I am not telling people to eat a specific diet by asking this nor am I claiming that a very low calorie diet is safe by asking this

Question
Presuming the same sleep and exercise routine

Which diet would cause someone to lose weight faster

Diet A
1500 Fat Calories
560 Protein Calories
0 Alcohol & Carbohydrate Calories

Diet B
560 Protein Calories
0 Fat, Carbohydrate & Alcohol Calories