FBAT-PC and FBAT-GEE are two approaches for handling multiple phenotypes in PBAT. Each has pros and cons depending on your specific situation.
FBAT-GEE is a generalized estimation equation and you are running a multivariate test. The biggest benefit to FBAT-GEE is that you can run multiple phenotypes that do not have the same distribution, e.g. dichotomous and continuous traits. Important to note with the FBAT-GEE approach is that an additional degree of freedom is added to the equation with every additional phenotype. Thus, it is not usually recommended to use more than 4-5 phenotypes with a single analysis.
FBAT-PC is a principal component approach to using multiple phenotypes. The approach is most powerful with repeat measurements over time (longitudinal data) and multiple continuous traits that describe a disease. For every SNP, PBAT maximizes the heritability of the principal component. Since an overall phenotype is constructed, you are never adding another degree of freedom to the model for your test. The limitation of FBAT-PC is that you can only run phenotypes of the same distribution, and in reality it is optimal to use continuous traits.
For additional details on FBAT-PC please visit the following article:
Family-Based Association Test-Principal Components (FBAT-PC)