I was not aware of anyone being offered a choice of punishment at our school.
In high school detention was rare, whilst the cane was used regularly. As someone who was not caned, I would have chosen detention. One reason was that the cane was semi-public, and I would have been apprehensive both as to my reaction and for other reasons. In contrast, there were more than a few who were given it regularly and appeared to revel in the status it gave them.