I received my more severe canings from the Headmistress (and one from the Deputy Headmistress) but I don’t think it would be fair to say they administered more painful canings than the Associate Headmaster.
As regards the implement used, the cane is usually considered more severe than the slipper but, in practice, I found that wasn’t always true. The cane was always seen as a more serious punishment but a severe slippering, especially off the gym mistress, could easily be more painful.