You're wrong. Mass has nothing to do (as much as is known at this time) with quantum effects being important or not. Quantum mechanics would (as far as we know) work the same for a 1kg particle as they do for a 1eV particle.

Instead, the difference is that the antiproton can interact with a proton and annihilate, while an electron can barely interact with a proton or neutron outside of the EM attraction.