I do both styles, both static and swing. With my high wrist recurve I use static, and with my hill style longbow I use swing. I have notice that with both there is still movement, and that is the rotation of the upper body while drawing, and I have been busted equally with both styles. I feel it has more to do with the range you are from the animal than anything else. the closer you are the less tolerance for movement.
All prey animals have three zones, recognition, flight, and fight. If you are in the recognition zone then them will acknowledge movement but will not run until they can identify it and adjust their flight zone. If movement is in their flight zone they will move away from it(quite often running) before they even try to recognize it. Their recognition zone and flight zone change with speed of movement, size of movement (standing or kneeling), and any sounds that are linked to movement
I believe this is why when you see older hunting videos where the hunter is moving and still have a clear shot at their animal is they are outside the animals flight zone.
The same zones are affected by sounds. That's why mature animals will move from a selected woods when they here a vehicle stop. The older and more wise the animal, the larger the flight zone.
That's just one mans very simplified explanation of prey animal responses.
Jesse