In most DFT codes like QE and VASP, spin-orbit coupling (SOC) can be incorporated by employing fully relativistic pseudopotentials. My question is with regard to the implementation of SOC among different functionals. If one believes that using a fully relativistic PP is equivalent to solving the Dirac equation, are the results simply transferrable between different functionals?
For example, let us say I calculate the total energy from DFT-PBE with SOC off and then turned on. The difference in these two configurations should give me the amount of SOC for my system. Now, if I perform DFT-LDA on the same system, should I expect just the same amount of SOC? My main concern here is because we use different pseudopotentials.