As someone that has done low carb diets that lead to ketosis, those 10 lbs are water weight. In short, carbs will make you store water weight (via glycogen).
You will not lose weight faster while in ketosis. You will lose fat faster. When in ketosis, your body uses fat almost exclusively for energy whereas on a low calorie "normal" diet, your body will raid fat and muscle. So weight loss is similar, but you'll retain more muscle on a super low carb AND high fat diet. A high protein diet with low carbs and fat will not lead to ketosis. Your body will convert protein into carbs when this done.
I don't know if it's necessarily healthier, but I feel better while in ketosis. YMMV