Phyllida just sounds hideous and although I am not a fan of Phyllis, I think it would be refreshing to hear but I personally wouldnt use it. It is very dated.
I liked Phyllida when I thought it was prn fih-LEE-duh but now that I know it's prn FIH-lih-duh I think I prefer Phyllis. Phyllis has actually been growing on me. It sounds more poetic than old-ladyish to me now.