One of the things that affects my son?s confidence at school is change. Every year when he moves into a new class it takes him a while to get use to the new things: children, teacher, classroom, etc. This year he found it much easier because one of his best friends was put in the same class and so he settled down in about half the usual time. (I intend to make sure he has a friend in the class next year too.)
If your child also gets upset with changes then even though he might be a bit bored he might actually prefer to stay in the same school. If, however, he enjoys the challenge of change and exploring new things, as my other son does, a new school might be a better option.
Best wishes,
Barb