Both solve the same task, but the Rigby can give you a little more oomph/energy/KO-value etc. Whether that is really needed on a DG hunt is a different question. If a situation calls for something bigger than the 404J, the answer probably isn't the 416Rigby, but something along the lines of 458 Lott, 470 NE, 500 Jeffery or 505 Gibbs.
Component availability is probably better for the .416, as there are a handful of cartridges that uses .416 bullets, but only the Jeffery uses .423 (apart from the 10.75x68, and a few others that are quite obscure/obsolete).