Snape had already told Voldemort about the prophecy, or at least half of it, so what is the point of seeking that prophecy once again? It doesn't seem to have anything that would have been helpful for him to defeat Harry.
Voldemort didn't know that it held no useful information to defeat Harry. What he did know was that he had been defeated by a baby, who was the likely subject of the prophecy (Neville Longbottom being the other potential subject).
He wanted the prophecy so that he could know fully what it said, in case it held any information that would have helped him. He was aware he had only heard part of the details, and given the "defeat" by Baby-Harry, was keen to know the rest in case it gave him a clue how to avoid a repeat of that outcome. He didn't know that it wouldn't help him; and Dumbledore quite possibly thought it worth keeping secret to try and force Voldemort to reveal himself to the public when he tried to get hold of it.