This is my opinion:
Madonna is the best songwriter and has co-writed most of her songs, while Cher's discography is mostly written by others: she suffers from dyslexia, apart from starting her career in a time when no label would let a woman write her own music, or be independent in her career (that's why she started as Sonny & Cher with her husband back in early 60s). Despite of that, Cher has released her album Not.Com.Mercial written entirely by her.
Cher is the best actress - she holds 1 Oscar and 2 nominations, 3 Golden Globes and 6 nominations and 0 Razzies.
Madonna is the best dancer. Cher has never danced in her tours, or videos.
Cher has the best live voice, stronger and more powerful and versatile. It fits better with her country-rock music, while it can sound weird in her pop records. Madonna's voice is good for the music she makes.
All in all, both are talented and have their strong and weak points. But I prefer Cher.