I suspect the cane hurts more on the bottom to start with because the caner is confident to use full power straight away. When starting to strike the smaller target of the palm, the natural instinct would be to hold back slightly and take a little more care. It also depends on the density of the cane. “Hard” canes, those that do not reflect any of the impact back up the shaft to the caner, really rattle the bones and joints in your hand and are excruciatingly painful, six strokes can be almost unbearable. Probably the tawse you have experienced is very dense rather than spongy, with a similar outcome.