Conditions matter and your reaction should always be for the worst possible scenario (moose and snow), braking removes your ability to maneuver as well, and locking the brakes up which will almost always happen when you panic break, would be the worst scenario. If there’s snow or rain, braking again is right out.
If it jumps out and you can’t do anything but brake, you shouldn’t do that, you grip the wheel and maintain speed, and if you can punch the gas for the hood raise. But people panic and can’t think. So maintain speed, don’t panic and lock your brakes up.