Are peregrine falcons faster than bald eagles?

No, bullets are fired at an amazingly high speed. It can be difficult for even high speed 1200 FPS (frames per second) camera to catch a glipse of a bullet leaving a barrel of a weapon. Bullets cannot be seen by the eye either.

Peregrine falcons, even at top speed, can still be seen by the human eye and would appear to be moving in slow motion on a 1200 FPS high speed camera. They are extremely fast, but no animal is as fast as a bullet.