Tolkien's clearest statement on the Rings suggests that all of the Rings made in Eregion with Sauron's help, both Great and lesser, differed at most in potency; it was only the Three made solely by the Elven-Smiths that were really unlike the others.
The chief power (of all the rings alike) was the prevention or slowing of
decay (i.e., 'change' viewed as a regrettable thing), the preservation of what is desired or loved, or its semblance -- this is
more or less an Elvish motive. But also they enhanced the natural
powers of a possessor .... And finally they had other powers, more
directly derived from Sauron ... such as rendering invisible the
material body, and making things of the invisible world visible.
The Elves of Eregion made Three supremely beautiful and powerful
rings, almost solely of their own imagination, and directed to the
preservation of beauty: they did not confer invisibility.
from "The Letters of J. R. R. Tolkien"
This passage suggests that the later a Ring was made, the more potent it was: the Three Rings, made after Sauron left Eregion and therefore without his help, were nevertheless "supremely powerful" because the Elven-Smiths had become more skilled in ring-making. Gandalf says much the same:
In Eregion long ago many Elvin-rings were made, magic rings as you
call them, and they were, of course, of various kinds: some more
potent and some less. The lesser rings were only essays in the craft
before it was full-grown...
from "The Shadow of the Past" in "The Fellowship of the Ring"
Were some of the Seven and the Nine, then, more powerful than others? It seems likely, but perhaps not markedly so. Certainly any differences in strength between them were not nearly as large as the differences between the Great Rings and the lesser rings.
Per Saruman (as recalled by Gandalf), the Rings of Power -- with One notable exception -- were different in design from the lesser rings:
"The Nine, the Seven, and the Three," he said, "had each their proper
gem. Not so the One. It was round and unadorned, as it were one of
the lesser rings..."
from "The Council of Elrond" in "The Fellowship of the Ring"
The final chapter of "The Lord of the Rings" describes the Three Rings as each having a gem of a different color; Galadriel's ring is in addition made of mithril, implying the others were not. Likely enough the Seven and the Nine also differed from one another to at least some extent in ring material and gem.
Addendum: it's specifically mentioned of Thror's Ring -- and by extension, all of the Seven -- that it had an ability to multiply wealth:
Of the Ring he said to Thrain at their parting: 'This may prove the
foundation of new fortune for you yet, though that seems unlikely.
But it needs gold to breed gold.'
from "Durin's Folk", Appendix A, Part III to "The Return of the King"
It is said that the foundation of each of the Seven Hoards of the
Dwarf-kings of old was a golden ring...
from "Of the Rings of Power and the Third Age" in "The Silmarillion"
The One would also have had this ability, the Three certainly would not. It's not stated whether the Nine or the lesser Rings did.
