Hey, Football Junkie! Nice to see you!!
My own observation has been that the thinner the implement, the more it stings, and the thicker the implement, the more you get a "thud" effect.
The cane W and I have is very thin, which means it's almost all sting, but doesn't leave the kind of "track marks" that one expects from a cane, because it doesn't hit all that deeply. The times that W's used a thicker cane-style implement, it didn't sting as much, but the pain lasted a whole lot longer.
Those with a greater variety of experiences with canes can probably chime in with more info.