Coming from South London, it seems like every train is on the Bank branch (I have to change at Kennington 9 times out of 10).
Northern line trains on the Charing Cross branch only go south of Kennington at peak times. This is shown on the map of the Northern line but not on normal Tube maps.
My guess is that there are equal numbers of trains via Charing Cross and via Bank, but the morning trains in via Bank are much more crowded, as more people work there. More capacity would help, either way.