You are asking about the difference between the traditional Japanese and Chinese methods of soy milk preparation.
In the Chinese, the beans are soaked, ground, strained, and the milk is boiled.
In the Japanese, the beans are soaked, ground, boiled, and then strained.
I have tried both ways.
The Japanese method extracts more from the beans but they tend to foam a lot while they boil. Depending on your straining setup- you will also have to wait for the beans to cool before straining them.
The Chinese method is faster because I don't have wait for the beans to cool. Additionally, if I am making tofu I can add the coagulant immediately while the milk is hot.
I was not able to detect a difference in the resulting milk. I now use the Chinese method because it is faster and easier for me.
I have not read of or tried cooking the beans whole before grinding- I assume it would result in much lower yield and have the same downside as the Japanese of requiring the beans to cool before I can work with them.