Both of them are spectrophotometric methods, which are used to investigate the in vitro antioxidant capacity of foods and biological samples. They are based on electron transfer reactions, which visually results on the reduction of a coloured oxidant (DPPH or FRAP as oxidant). Therefore, usually the results obtained from these methods present excellent correlation.
I believe the main difference is that DPPH is a stable organic nitrogen radical. The reaction progress between the radical and the antioxidant is monitored for aproximatelly 30-40 minutes at 515-517 nm, or until stability. So, we must be careful with antioxidant compouns such as some anthocyanins that absorb at similar wavelenghts and could interfere in the final results.
In the case of FRAP, there are no free radicals. What is monitored is the reduction of ferric iron to ferrous iron in the presence of the antioxidant. This is usually done every 15s until 4 minutes, at 597nm. For some polyphenols, FRAP values cannot be accurately obtained after this time.
The file article attached (The chemistry behind antioxidant capacity assays.) may be helpful.