Well, by implication, although not by actual denotation, the three were different from all the rest. Celebrimbor made the three, and he never was willing to associate with Sauron. Evidently it is inherent in the nature of such rings that a greater ring can overcome them, and rule the wearer of the lesser. But the intent of the creator does seem to have some influence over the result. The three were not made to dominate, but to preserve.
Other smiths in Eregion made the other sixteen rings. Those smiths worked closely with Sauron, and were strongly influenced as well. I think the seven and nine were essentially similar in nature, magnifying the inherent power of the wearer, and linking his will to the will of whoever wore the One. The fact that seven were given to dwarves was just a numerical fact, not a planned set of recipients. I think each smith made his ring, or rings for his own purposes. Perhaps those purposes varied, and the skill of the smiths as well.
I think the effect on the wearers varied because of the nature of the recipients, not the nature of the rings. A very powerful human sorcerer or king became a much more powerful, and daunting personal presence, yet all the while, that human’s spirit was bound, and enslaved to the will of Sauron, wielding the One. A dwarven lord became more skillful in his crafts, for craft is the nature of dwarven hearts. He also became more greedy for the fruits of such labors, his own, or another’s. The presence of the One ring, and the ability it had to impose the will of Sauron upon the wearers of the others worked well on men, because of the inherent nature of men, rather than the inherent nature of those particular rings. Dwarves, had spirits so entirely different from the spirits of either Men, or Elves, (Or Maia, for that matter) that the intended enslavement was not possible. But the rings still followed the will of their master, rather than the will of their wearer. So the hearts of Dwarves were inflamed, and their greed accomplished what enslavement could not and one by one the Dwarven Lords died.
Ents, I think would be uninterested in such things as rings, or swords, or staves of power. The power of Ents is the same power that is in the Earth itself. I don’t think the rings would have any effect on an ent. Besides, they wouldn’t fit.
Orcs, trolls, and such would be magnified according to their stature. The stature of an orc being what it was, I doubt that a great ring would allow them to do much more than become one of the kings of orcs, perhaps the greatest of them, but orcs are quintessentially subservient to greater power, and there was no shortage of that in the realms of Sauron. Probably turn into nasty quasi-nazgul, big on horror, weak on actual power.
We hear nothing about the original elves that made these rings, aside from Celebrimbor, and we must assume that they either were killed for them, or gave them up willingly, once they were able to see what they had done. Elves evidently don’t make good servants.
Tris