RE-LOCAL will give results slightly different to those from MOPAC because of two reasons:
(1) Sets of LMOs that could be resolved into banana bonds or rabbit ears are not resolved. This means that such LMOs are ill-defined, however this would never be significant in reactions.
(2) The unitary rotation of the occupied set will not allow atoms to be created. So if one LMO has a specific atom that is not present in another LMO, then rotation of the two LMOs will result in the loss of wavefunction in the second LMO. This is also never important but in this case because the loss only occurs in the tails of the LMOs.