For all intents and purposes both cartridges achieve prety close to the same performance, and both will hammer big animals with plenty of authority.
However, if I were to pick one to build a rifle around, it would be the .404 Jeffery, as it can be housed in a lighter action, and will therefore be a lighter rifle.
When you get to be my age, with a bad back, hauling around a heavy rifle all day can be quite a chore!
