When weight is lost through caloric restriction, a higher protein intake is usually seen as a good idea due to preserving lean mass during the weight loss period.
A study that stratified gender found that a 500kcal dietary restriction for one year resulted in 9.9-11.2% weight loss in overweight persons with no difference between gender and overall weight lost did not differ between the high protein group (1.6g/kg) and the low protein group (0.8g/kg); when measuring only fat mass, the high protein group lost significantly more fat (14.3 ± 11.8%) than did the low protein group (9.3 ± 11.1%) when calories were kept equal.  This study found that higher protein benefited both men and women, although men inherently lost more weight as a percentage of body fat. 
Protein and weight loss is also important for postmenopausal women and older men, as caloric restriction-induced weight loss appears to inherently reduce lean mass, with more lean mass being lost when dietary protein is lower despite caloric deficit being similar.  When investigating older (65.2 ± 4.6) women who are either overweight or obese and given a diet consisting of 1,400 calories (with a set amount of calories from each type of macronutrient) the addition of 50g whey protein twice a day to this calorically restricted diet induced more weight loss (-8.0% ± 6.2%) than did adding 50g carbohydrate (-4.1% ± 3.6%) despite calories being the same.  The protein group lost slightly more muscle as an overall percentage secondary to weight loss, but gained when measured relative to body fat losses.  Another study comparing 15% protein (in relation to overall calories) against 30% protein found that the low protein group lost more weight (11.4 +/- 3.8kg) with 37.5% of it being lean mass, while the higher protein group had a slightly lesser rate of weight loss (8.4 +/- 4.5kg) with approximately half as much lean mass lost (17.3%).  These results are repeated in various trials with similar results, with higher protein reducing losses in lean mass associated with diet regardless of source.    Even a small trend towards greater consumption of protein and dairy foods is associated with more favorable body composition changes during weight loss in the older population. 
Consumption of protein in the higher range, usually seen as around 1g/lb of lean mass (if you know your body fat percentage and can calculate lean mass) or 25-30% overall calories, is more protective of lean mass during periods of intentional weight loss when calories are controlled for
One study conducted over 12 weeks comparing low (1.1g/kg) against high protein (2.2g/kg) found that the high protein group not only lost more body fat mass (with no significant differences in overall weight, due to muscle retention) but the high protein group also experienced a reduction in LDL cholesterol and total cholesterol not seen in the low protein group.  A high protein diet (34% of calories) against a high carbohydrate diet (17% protein) also appears to be more effective at reducing triglycerides, and is seemingly more effective for both health and body fat reduction in those obese persons with high baseline triglycerides.  
The above studies tend to control for overall protein intake, rather than sources. They can be used to argue that protein per se helps with fat loss and muscle preservation with little to no difference when comparing one source to another.
When looking at the quality of protein sources in other studies, those that tend to have a higher percentage of essential amino acids tend to be more well correlated to inducing fat loss;  this appears to extend to bone health as well.  These sources tend to be animal sources; meat, fish, eggs and dairy. It should be noted that the protein supplements of whey and casein are two common protein supplements and are both derived from dairy (specifically, dairy protein is about 80% casein to 20% whey).
Overall, protein per se takes precedence. Beyond that, animal sources tend to be better than plant sources due to a higher percentage of essential amino acids
For a more detailed analysis, see our article on ideal levels of protein consumption based on your goals.
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