For Southern CA, including the Santa Barbara-area boarding schools (not sure about the Bay Area), the ISEE is most prevalent. For the East Coast boarding schools, most request the SSAT, but they are also open to accepting the ISEE. My son only took the ISEE and submitted it to both Southern CA and NE prep schools. He was a successful candidate.
If I remember correctly, you can only take the ISEE once every six months. The SSAT, on the other hand, can be taken multiple times.
Admissions staff said it was fine to take both tests. They want the best score.