As far as how stressful it is, I'm sure its comparable to a clinical psychologists. Also, school psych PhDs can practice in clinical/medical setting so they can share in the clinical stress.
Paper work and parents are a reality that all practicing psychologists (or any child health care provider) has to deal with. Also, clinpsycmasters pointed out the push and pull forces of the agency vs. the patient vs. yourself. Keep in mind that those also exists in any arena of practicing psychologists. Now is it MORE of a headache for school psychologists? The answer is... it depends.
So the things that others have mentioned are indeed drawbacks, but they are realities all psychologists put up with to one degree or another.
One thing that is specific (and like lookitssara aptly pointed out it varies on distract) is that school psychologists have to go from one school to another. I once shadowed a school psych that essentially kept her office in her car because she had to drive from school to school so much. In the same vein, how you are treated and seen may vary between schools. Some schools might see you as bother, while other view you as an integral member of the team. Whereas if you were working in a hospital, for example, you adjust to the ONE climate, as a school psych, you may have to adjust to many just in one day!