As a rule, a superficial partial-thickness burn is more painful than one involving deeper tissues. how would you explain this observation.

This is mainly due to nervous tissue density in regards to the layers. a superficial burn usually involves the outermost layers of the skin; the Dermis and Epidermis. The Epidermis being dead skin cells, does not have much in the way of nerves, which is why you wouldn't feel anything, if you say cut the skin so thinly, that no blood is drawn.

The Dermis, does have some tissues, but it's main duty is just to have enough to detect some painful stimuli and or touch, its relatively thin, and sometimes you don't feel things as much (This is the layer a diabetic's lancet is used to draw blood, sometimes you can feel pain, or sometimes you won't).

The main subcutaneous and muscular tissue, below the uppermost layers are full of vasculature and nervous tissue. So it can be assumed this is way more painful, and much more dangerous if burned.