I like Pandora more on both counts. Pandora's myth is about the conundrum of, like, knowledge? I also really like the sound and I think a lot of the nicknames are cute. It regularly makes it to the top of my list.
Persephone is almost appealing to me - I like the sound less, I like Persi and Sephie less than Pan/Panda/Dora. And the mythological Persephone is too extravagantly gothic for me to want to pin her name on a child. As I keep saying on this board, she was the underworld goddess - she isn't the goddess of both worlds, when she's above ground her name is Kore. Persephone is a dark halloween queen.