I'd take Joni Mitchell in a squeaker over Carol King, mostly because I prefer Joni's jazz-influenced style more than King's pop sound. It's a squeaker though because Carol King is a giant and wrote some of the best pop music ever!
I'd put kd lang in there, too, over Stevie Nicks, for her creativity and her vocal style, even though she was never as popular as Nicks in her prime.
Not sure if Patsy Cline wrote her own stuff or not. If she did, I'd put her in the pantheon of all-time greats. Amy Mann is great, too. Can't leave out Fiona Apple.
EDIT: OH, how could I have forgotten Patti Smith!
Janis Joplin, wrote some of her songs but most of the ones she was most famous for were covers. They were incredible, kick-*** interpretations, though!