When I started my search for a Buff/Elephant rifle the 404 was quickly ruled out simply because it was a Custom calibre at that time. Now it would be a toss up between the 2. Would I exchange my 416 Rigby for a 404J, no way. The 416 Rigby can be loaded up a little to become a 300mt rifle with 400grain pills.
While in Zim I ran into a SA PH who, when asked why he used a 416 Rigby said " I use this because I don't want to hurt animals, I want to kill them". Best recommendation I have ever heard.
Both are very capable cartridges and you won't go wrong with either one.