Why is an electron affected more by interacting with a magnetic field than a proton?

The masses are different. While both the proton and the electron have charges that are approximately equal in magnitude (though opposite in actual charge), the proton has a much greater mass. This means that while the magnitude of force from the particle moving through a magnetic field will be the same, the electron will have a greater acceleration due to it's smaller mass. Just to give an idea for scale, the electron is approximately 1/1836th the mass of a proton.