I guess you are assuming both particles are moving through the magnetic field at the same speed... because if you were assuming they had the same (kinetic) energy this would not be the case (same behavior)
Well it depends on how far you want to go with the explanation: it is simply because of Lorentz force at the most basic level (F
) that creates an acceleration transversal to the both field direction and the particle's velocity. In turn this effect can be explained (at least in some cases) as a relativistic effect on the electric field as it is perceived by the particle in motion. In its rest reference frame there might be no magnetic field but the inertial observer would observe one and explain the transversal acceleration as due to it. From the particle's point of view no transversal acceleration would exist and everything would be explainable in terms of coulomb's law...
Hope this helps, Dario