I thought the ballistics of the 450/400 and the 404 Jeffery were the same. With the 450/400 being used in a double rifle and the 404 Jeffery is a bolt action.
@Shootist43 You've got the score figured out. There are many rimmed/rimmless twins in this world.
7x57 / 7x57r
7x64 / 7x65r
450-400 / .404 Jefferey
375H&H and 375HH Flanged
318WR / 318 Flanged
Most Rigby calibers and a rimmed "Rigby Number 2"
The list gets very long but here is the really important part. When doubles were born, they were using either blackpowder or they were using stranded cordite loads. The load data can be viewed to this day but it references 1926 ICI and 1921 Kynoch load data with pressures and velocities. Add to that, the proof barrels were 28" so the regulating load was never witnessed in a real-world 24-26" barrel. Compound that by the fact the original load data all lied favorably by 35fps to 75fps.
Now that we understand the lies and omissions of the original data, imagine a 1921 pair of rifles, one 450-400 3" and the other 404 Jeffery. Even if both were loaded the same in that moment (semi-lethargic) the 404 was a magazine rifle cartridge so they could cheat at later dates by giving it a bit more oomph, or a larger bullet, or a change of powder to obtain more zip. The double rifle was stranded, stuck, ummovably damned to the original regulation load because that ammo was used and the regulating wedge of the barrels was adjusted until close to perfect. Any attempt at a later date to change powders, charge weight, bullet weight, or other "hotrodding" of the rimmed cartridge would have ended in futility. So over time, we've seen the rimless cartridges evolve into formidable, highly efficient weapons with better components whereas the rimmed versions had to stay just as they were for a century.
Today, they no longer match each other whatsoever. Even more advancements (e.g. 404 Jeffery 450gr bullets zipping along while producing nearly 60lbs of felt recoil rather than the original 38-42lbs) have made the schism between rimmed and rimless even more apparent.
The only exceptions to this are a problem in and of themselves. You can find super over-powered modern double rimmed ammo out there that his wholly unusable in vintage doubles. You can order a brand new custom double rifle regulated for this way-over-the-top rimmed ammo. The problem is, no other ammo is likely to regulate in that double and you will struggle to find a regulating load if your hotrod factory rimmed ammo manufacturer changes their recipe or discontinues the product. Examples of this disaster occurring include 1990s Federal changing their load, Wolfgang Romey in Germany, and others.
So what's someone to do with all this data? Buy a larger double rifle caliber than you think you need in rimless equivelant. Handload for your double rifle to see if you can get another powder and bullet to regulate as well.
In my real-world example, I have a Heym 470 Nitro made in 1999. It will flawlessly regulate using 107gr of IMR4831 that is a hell of a potent load. (ouch) OR it will load to regulation with a near perfect-copy of the original velociites from 1921 using IMR3031, a near perfect reproduction of the Stranded Cordite load a century ago but using only about 77gr of powder. (hugs and kisses loads) So do I want to get beat to hell by my heym approaching weatherby type recoils, or do I want a mild original load that gets me the same recoil as a standard .458 Win mag, about 58lbs? I want the mild, manageable load. I'm damned lucky I have a choice, most people with doubles don't get two choices by stroke of luck, they get what they get with the one load that works with a single powder. That is very unfortunate if it happens to be a 1921-era 450-400 3" regulating load and they want to kill an elephant because that just isn't optimal, yet a brand new .404Jeff magazine rifle will be more than sufficient.
Hopefully my long response sheds light on the similarities and differences of Rimmed versus Rimless twins and why they are different.