I like Phoebe better. Even though Clementine is cute, I wouldn't want to be named after a little fruit. You know?
I agree with nat108, Phoebe does sound very childish to me. Also Phoebe's such a perky name that I can't imagine it on someone who turns out to be a pessimist.
At first my problem with Clementine was the nicknames- I hate Clem and Clemmy- but then when I heard Minnie, Emmi, Min I started to like the name a lot more.
Also Clementine makes me think of the little girl from the Walking Dead game, who is completely adorable. If you can't picture Clementine on a little kid, look up the game.