College and University - Education
Grade school and high school teachers may be dealing with pretty basic knowledge, but their jobs are not easy. In fact, education is a highly regulated profession, and as such it has a lot of standards to follow. For this reason, teachers cannot be deemed teachers without proper education.
Yes, educators also have to study education first before they can teach. In education courses, students don't just study the different subjects taught in school. More than that, they also learn about teaching methods, theories, and best practices that can be applied in schools. Teaching methods are different, especially depending on which age group is being taught. Different grade school levels require various teaching techniques. Also, high school is an entirely different story.
Handling children is a pretty daunting task. Not only do teachers have to make sure that their lessons are simplified enough for kids to grasp, but they also need to deal with kids' temper tantrums, misbehavior, bullying, self-esteem issues, and many other things. It can be stressful to teachers, which is why they must be trained well in how to handle these things properly. Education courses are designed to equip students with the appropriate skills they need to manage naughty children.
Curriculums are also quite different depending on year levels. So there are separate courses for pre-school education, primary education (first grade to sixth grade), and secondary education (high school). As the levels of maturity of the kids are also different, the teaching methods and theories covered in each course are also varied.
As to which one is tougher, it depends on the person. Each course has its own set of challenges. For example, in primary education, the lessons are easier but handling kids that age is more challenging. On the other hand, high school has more complex lessons but kids are more mentally mature, so handling high school kids may be easier.