Methinks2600 fps withthe RemMag yes, with 400 grain bullets no.
Perhaps a bit more than 5 fps between the Rigby and the RemMag.

Barnes #3
400 grain XLC's

416 Rem Mag:
2363 fps

416 Rigby
2673 fps

310fps difference when you are talking 400 grain bullets is a lot of differential.

How is it possible? One answer. Case capacity. RemMags are usually stuffed while Rigbys have lots of room. I've heard of folks attempting to maximize RemMag performance only to find that the seating of the bullet on a compressed round bulged the shoulder suffiently to where the round would not chamber in the gun. Even on max loads for the 416 RigbyI can still hear the powder shake inside.

The Rigby shares more in common with the 416 Weatherby than with the 416 RemMag (compare the cases and you'll see that Roy wasn't all that creative).
Not bad for a 95 year old Brit.

Yes, one can always drop to smaller bullets (the 325 Barnes X is no longer made BTW) and then the 416RemMag closes the gap a bit, but always lags behind.... sometimes a little, sometimes a lot.

BB, don'tget aBigBore for economy of anything, it's akin to buying a 4x4 Dodge 1 Ton truck with the Cummins Turbo Diesel and then whining about the cost of diesel fuel --- bullets, powder, etc.... same story.....

If you reload, or are supplied by someone who does, thenthere is potential for more than 5 fps differential.
That said, the 416RemMag is a powerful and popular option.
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All this is very nice but still doesn't answer BB's original question.