These 2 specializations are very close to each other. Between 1995 & 2000, the Open University (in my country) gave me the "secret, then" duty of preparing exams & assignments in both organic chemistry & biochemistry although my field of study is (Organic Chemistry of Polymers & Polymer Technology).
With so many chemists doing postgraduate studies in organic chemistry, there will be limitation to their recruitment for jobs so my advice is to go for biochemistry which is expected to have more opportunities in the future specially if students choose "Applied Biochemistry" which is taught in developed countries.