Two proton beams going in the same direction repel each other whereas tow wires carrying currents in the same direction attract each other. Explain.

The magnetic field is not as strong as electric field and the magnitude of magnetic field due to a moving charge only equals that of its electric field only when the velocity is equal to the speed of light. So for two protons moving in the same direction, Force due to electric field repulsion will exceed that due to magnetic field attraction. So the proton beams moving in the same direction repel each other.

But two parallel current carrying wire attract due to magnetic attraction as the electric field is inside the conductor and is shielded by it and can’t be felt outside. The magnetic attraction can be further reinforced by Fleming’s left rule by considering the magnetic field produced by one wire and electric field in the other wire in the direction of current.