Currently the limiting factor on a man portable rail-gun is several things, first and foremost providing enough energy to fire one. Conventional ordnance stores the energy in chemical form, which is energy dense (4.6MJ/Kg for TNT) whereas the batteries required for an electrical rail-gun are far less effective (at most 0.46-0.72MJ/Kg). Assuming a ten fold increase in battery capacity, rail-guns would be very competitive.
Having a portable energy source such as miniature fusion reactor would be much harder to develop, but this would allow much higher energy densities (576TJ/Kg for Deuterium-Tritium, ignoring the weight of the reactor).
Rail-guns also suffer from rapid wear caused by the severe friction during firing. This would either require more resistant conductive materials, or more frequent barrel changes than conventional ordnance (but not a huge challenge).
As for effectiveness, we can compare (as another question did) to the Carl Gustaf. If we assume all of it's ~4kg projectile is TNT or equivalent, it would have an explosive force of ~18.4MJ (and we can assume kinetic energy is minimal). This compares very favourably to 20MJ in your specification for the rail-gun.
In short, with improvements in battery or other portable electrical supplies, a rail-gun is a very feasible option.