How did the Seven and the Nine differ?
We’re not sure; possibly there was no difference. It’s easy to see that the Dwarves did different things with the Seven than Men did with the Nine. Sauron could not dominate the wills of the Dwarves through the Rings, nor could they be turned to wraiths. The main effect seemed to be to intensify the standard Dwarvish greed for gold, which of course provided plenty of occasion for quarrels between Dwarves. Men, on the other hand, became great kings and sorcerers on their way to becoming wraiths [Silm: Rings (288-289)]. Those seem like differences between Men and Dwarves, not between two groups of Rings. Several quotes imply that Sauron just took the sixteen Rings he got from his war on the Elves and handed some to Dwarves and others to Men. For instance: “Sauron gathered into his hands all the remaining Rings of Power; and he dealt them out. … Seven rings he gave to the Dwarves; but to Men he gave nine, for Men proved in this matter as in others the readiest to his will.” [Silm: Rings
