My take on it is that both don't have anything against desires.
LOA teachings tell you to embrace your desires because that's all what you - as focusing mechanism - are here for. Going against them would go against you nature.
Original Buddhism tells you that you are not the one who desires but the one who witnesses the one who desires. You are not that focusing mechanism, that's just a temporary identity. Therefore it is irrelevant what happens to those desires. And going against desires would be taking this temporary identity for real and that's the cause for suffering, not the desires.