It is not just the question about the rimless vs the rimmed, there are more things to consider.
Doubles share the same break open action as shotguns. This means they do not have a strong extraction system such as bolt actions. Cases or cartridges have to be lifted out of the chambers by opening the action and the ejectors/extractors, come into play once the cartridges have been initially lifted.
In order to function perfectly in a double rifle, a rimless cartridge needs a specially adapted extractor and/or ejector that contains a small spring-loaded blade which pops up into the groove at the base that all rimless cartridge cases have. This occurs when the action is closed. If for some reason this system fails, the rifle will not extract and/or eject the cartridge case, period. Westley Richards perfected this system but it has it's limitations.
Rimmed cartridges are much better suited to double rifles because the extractors and/or ejectors have a much larger surface (the rim of the cartridge case) to grab hold of for case extraction/ejection. They do not rely on tiny little springs and two blades (that are really quite small), to function.
Belted cartridges use the belt for head spacing.
Rimmed cartridges can headspace on the rim, they extract better, work well in bottleneck or straight case alike, the only limitation on their strength is case design and the action the are chambered to.
The 458 Win mag and 458 LOTT both are rimless belted cases with straight wall cases. They both operate at about 50 percent more chamber pressure than a comparable Rimmed NE.
This extra pressure(especially on a straight walled case), can cause sticky extraction. The camming action of a CRF action can handle this in a good quality rifle. A double rifle system will have a hard time. 40 to 42 degrees celsius in the Zambezi Valley on top of that, eish! I do not want that 458 LOTT in a double in my hands when the chips are down! In a bolt gun, no problem. In a double, could be catastrophic.
Pressure:
458 LOTT operates at 62,500 psi with max 66,500 psi
458 Win operates at 60,000 psi with max 63,500 psi
470 NE operates at 41,000 psi with max 43,600 psi
For interest sake
577 Tyranasaur 60,000 psi with a max 63,800 psi
The big rimmed NE cartridges were made that way for more than one reason, rather stick to them and you will not have any issues.
I would only consider Rimmed cartridges for a double rifle, rimless according to Murphy will fail when you do not need it to and may well cost you your life or somebody in your groups.