What is the difference between Biochemistry and Chemical biology majors? What are the difference emphases of the majors? What type of career fields would these majors lead into? Is one major more rigorous than the other? Does one allow for more flexibility in the classes required to take?
The distinction and differences will be school-specific. Look up the degree requirements for each major at each school of interest.
Probably the difference is that Biochemistry is in the Chem Dept and Chemical Biology is in the Biology Dept. Which department interests you more? Look on college websites about future job posibilities.
Jobs directly related to your degree include:
Analytical chemist.
Biomedical scientist.
Healthcare scientist, clinical biochemistry.
Clinical research associate.
Forensic scientist.
Physician associate.
Research scientist (life sciences)
Scientific laboratory technician.
This is actually the opposite at Berkeley, where chemical biology is run by the chemistry department while biochemistry is a subarea of molecular and cell biology.
https://chemistry.berkeley.edu/ugrad/degrees/chembio
http://mcb.berkeley.edu/undergrad/bmb