Why is it important to have the sympathetic and parasympathetic nervous systems, especially since their action?

Because they are responsible for automatic functions in your body, like heart and ventilation rate, urges to go to the bathroom, perspiration and production of saliva, contraction and dilation of pupils, etc.

Usually they are antagonistic (Sympathetic operates more under stress while Parasympathetic doesn't) but it's not ALWAYS the case.

Also of note, many of the instances in which they are antagonistic, they will not operate by giving opposed stimuli to the same effector but rather both might stimulate opposing effectors, etc.