I think they're both pleasing names.
Phoebe perhaps sounds a little more American to me because of the Friends association, however that will probably fade with time.
When I think of Abigail I associate it with more historical origins:
In the bible, she was the wife of Nabal, who saved his life, he died and David married her for her good qualities. So that might possibly temper any Abi Titmuss bad girl connotations! Or not?
Abigail Adams, First Lady, married to John, one of the US presidents in the 18th century, apparently known for her keen intelligence.
There was a Baroness Abigail Masham, favourite of Queen Anne and cousin of Sarah Churchill, Duchess of Marlborough.
Oh and there's Abigail's party, the entertaining, 1970's play about class interplay. Crucially, the teenage Abigail is never seen, only spoken about quite briefly. Her mother, Susan goes to a neighbour's house where a few neighbours enjoys drinks party whilst her daughter is having a party of her own at home. This is shamelessly copied and pasted from Wiki! "Susan represents the upper middle class, Beverly and Laurence the aspirational middle middle class and Tony and Angela the "new arrivals" and lower middle class. The comedy arises from Beverly's inept attempts to help Angela and Tony, which have their roots in her sense of class superiority, and Susan, which has it roots in the fact that she is married...Several critics (notably Tom Paulin[1]) have responded more negatively, noting that Abigail's Party appears to represent a middle-class schadenfreude, with the only true middle class character, Sue, looking on at the antics of the couples with disdain.
I think there might also be a feisty schoolgirl with the name in Skins too.
They're both great names. I lean towards Abigail a little more personally. Depends on how it sounds with your surname too.