let's compare their pure solo #1's:

Rihanna
1. S.O.S
2. Take A Bow
3. Disturbia
4. Rude Boy
5. Only Girl

Mariah Carey
1. Vision of Love
2. Love Takes Time
3. Someday
4. I Don't Wanna Cry
5. Emotions
6. Dreamlover
7. Hero
8. Fantasy
9. Always Be My Baby
10. Honey
11. My All
12. We Belong Together
13. Don't Forget About Us
14. Touch My Body

S&M by Rihanna is excluded because it ONLY reached #1 because of the release of a last minute remix which featured another artist.