I have fired a 416 rem some,and the recoil felt about the same a a 31/2 Ten gauge mag load in a light break action single shot shotgun.I might like it if I really needed it,but it was a bit much for me.
I have,however,fired someone's home made scaled up rem 700 in 50 BMG and wanted more!!
I think there is something to pressure level and the characteristic of recoil.
I can tolerate being pushed,but being punched is more painful.I don't know for sure,but I suspect in equal rifles ,even with similar ballistics and the physics of how mant ft lbs come through the butt plate,the acceleration and felt recoil of the Rem might be more.
The CZ .416 actions are in Brownells,I think the Montana Rifleman makes a .416 size M-70 clone.
Looking to see if a 338 ultramag was catalogued in a Sendero (prairie dogs)
I could not find any Rems over .300 Ultramag in any rifle outside their custom shop.Then the price starts at about $3000
As the Rem extractor is not favored for dangerous game,I suspect the Rigby will be easier to find ammo for,long term.
And,while I have never held or fired a .404 Jeffreys,for some reason,I think if I chose an exotic far away places rifle....