A Rigby is never ill advised, however the secondary market for a Big Game in 416RIGBY vs the same rifle in 404J...there is a significant price difference.
If a person were at W.J. Jeffery & Co and ordering a rifle, would they even consider ordering a 416RIGBY? Of course they wouldn't because they don't even offer their rifle in 416RIGBY. Frankly I'm surprised that Rigby offers their rifles in the 404J.
Tell you the truth, I'd really love to have a Holland & Holland London Best 375H&H magazine rifle.
With the Heym rifle you could have either cartridge and no worries about not having the maker match the chambering.
Of course, it's your rifle and you can (and will) do as you please.