Whey and casein are derived from milk sources, whilst soy is derived from the vegetable. Interestingly, both soy and milk proteins are "whole proteins" - containing the full spectrum of amino acids required by the human body. However it is now commonplace amongst the bodybuilding community that milk (particularly whey) is a more effective protein at assisting muscle gains following a workout.
A very interesting study was conducted by McMaster University’s Department of Kinesiology and was recently published in the American Journal of Clinical Nutrition. They compared milk protein to soy protein following a weight training workout. (Milk contains approximately 20% whey protein and 80% casein protein.) The men that consumed the milk following their workout gained almost twice as much muscle compared to the soy protein group over a 10 week period. Their conclusion:
Milk-based proteins promote muscle protein accretion to a greater extent than do soy-based proteins when consumed after resistance exercise. The consumption of either milk or soy protein with resistance training promotes muscle mass maintenance and gains, but chronic consumption of milk proteins after resistance exercise likely supports a more rapid lean mass accrual.
Similar results have previously been demonstrated in several other studies too.
However when considering soy versus milk versus whey versus casein, whey isolates have been shown to be extremely effective:
Soy protein is not a very effective protein to consume following a resistance training workout as demonstrated by the study above. The rate of absorption of a soy protein isolate (ie. that found in a supplement) is approximately 3.9g per hour which is relatively slow.
Milk protein is a whole protein and is thus absorbed by the body much slower than proteins such as isolates found in supplements. The rate of absorption is approximately 3g per hour which is again slow. However whole milk has been demonstrated to be more effective than soy.
Casein protein, a derivative of milk, is slowly absorbed over a 7 hour period, which is not very effective by itself, at assisting recovery immediately after a workout. Casein protein, in isolation, has been shown by many studies to be relatively ineffective at assisting protein synthesis post-workout. This is because your body is placed in a state of recovery and requires fast-acting nutrients.
Whey protein is a very fast absorbing protein that contains the full spectrum of amino acids. The rate of absorption of whey protein isolate (commonly found in supplements) is between 8-10 g per hour which is extremely fast. This aids the recovery process and thus assists protein synthesis.
There is however much more research to be done in this area. So no firm conclusions can yet be made with the lack of studies currently available.