Both schemes require a regularly evaluated and continuously improved upon: 1) food safety management system; 2) good manufacturing, distribution, and agricultural practices; and 3) HACCP system.
BRC is more prescriptive on procedures and guidelines to follow for food safety while FSSC 22000 emphasizes a framework approach—helping a business implement its own system. FSSC 22000 expands upon ISO 22000, so for organizations already down this path, it may make sense to continue with FSSC 22000 certification.