There is evidence of both idioms being used during the 1800s but it is difficult to say which came first. I have found evidence of the expression 'has a nice ring to it' from 1830. The word ring, in these idioms, alludes to a highly resonant or sonorous sound, as that made by a bell.

Has a nice ring to it meaning?

to have a nice ring: to sound nice, good, pleasing to the ear. idiom. I've always thought that the name "Susan B. Delavigne" had a nice ring to it.

What does it mean to have a ring to it?

to seem or sound like something you have heard or seen before: Her name had a familiar ring to it. I didn't know who was speaking, but his voice had a familiar ring.