Traditionally used in Native American smudging ceremonies, both are good for cleansing, purification and protection. They remove negative energy in a space, objects or people. The scents are quite different, but either is a matter of preference. I can say that most people come into my store wanting white sage.
White Sage: From California and is considered male.
Green (Desert) Sage: From the planes and is considered female.
Also consider my favorite: Sweetgrass
Also used in Native American ceremonies, it has a sweet smell (kind of like a Swisher Sweet cigar). As is the case with my feng shui practitioner friend, I have seen people use only sweetgrass as a form of purification and to call in positive energy. My Lakota friend uses it after sage smudging to call in the energies, or what you and I know as angels.
Sweet Blessings, Dianne