I think its important to note that the rings were not Dwarf rings, any more than the nine were Human rings - all of these were forged by elves but touched in some part by Sauron. They could have all had exactly the same powers.
What we do know from the text is what those 16 rings brought out in those who used them, comparably the effects on humans and dwarves, and that none of these lesser rings were offered to elves. We have no way to know what effect the three rings would have had if they were worn by humans, dwarves or hobbits.
Look at the effects of the 16 - they enable things highly desirable to the receiver. Humans desire unending life (the Downfall of Numenor), and dwarves dream of great wealth. Their desires are fulfilled, but in an awful way since they were tainted by Sauron. For the immortal elves, that desire is for their realms to be as untouched by time as they are (this worked very well in Rivendell and Lorien with the rings of Elrond and Galadriel).
Now I am speculating here, but I suggest that the lesser rings lacked the sophisticated elemental personalities of the three rings, much as the One Ring appeared as a lesser ring because it lacked any real markings; I believe all of these lesser rings shared the same powers.