Sort of difficult to compare a .577 to a 500/416. They make up into totally different rifles with very different ballistics and for frankly somewhat different purposes. The .577 is a truly up close fight stopper (with the heft and dynamics of a crew-served weapon), while the .416 makes into a wonderful, manageable general purpose double rifle that is easy to carry in the field - mile after mile, day after day.
The "newfangled" 500/416 is simply a .416 with a rim designed for double rifles (as
@spike.t notes - essentially a .416 no.2 - there is very little new under the sun). Though, considering how few Rigby Rising Bites Marc is likely to actually sell, sourcing 500/416 ammunition should be relatively easy. I have a set of barrels for my Blaser S2, and the rifle is accurate enough that I shoot a scope on it. We initially were going to regulate ammunition for it at 70 yards, but both barrels shoot MOA and a 4-shot LxR/LxR group is three inches at 100 meters. Pretty amazing.
It seems to be fairly popular among the K-Gun fraternity which is logical as it is one of the flagship rounds Krieghoff developed for their modern double rifle. The two make a very capable package as does the S2 dressed up as a .416.
To
@norfolk shooter 's original question, I think it is a perfect choice for a client's double rifle. At least the S2 and K-gun versions seem to be inherently accurate, and the rifle makes up into something somewhat more versatile than the standard .470 solution. For instance, my S2 weighs nearly two pounds less than its English .470 stablemate with no recoil issues. Nice.