OK, the short answer to your question in No.
Pressure ratings are simply a standard. BTW, if you check European MPA pressure ratings, you might find them reversed for .338 Win Mag and .338 Lapua, I don't know.
Pressure ratings take into consideration the SAAMI (in the States) dimensions of the case and the chamber. That's not the whole story, of course, as both brass and steel expand under firing, so barrel tenon diameter comes into play, as does the robustnes of the locking system.
Short range benchrest uses the .220 Russian case, necked up to 6mm, and blown out. Whatever the rating of the parent .220 case, many run pressures in excess of 70,000 psi. These are in custom chambers, where the chamber is *about* .002 to .003 over the size of the virgin case (all dimensions in inches). The case is .440 in diameter, and used with barrel tenons at least 1.00, usually 1.125. Take the same tenon diameter and use a case with .540 diameter, and a whole different story would emerge.
Think it through. Pressure ratings are primarily to specify the life of the brass case, and moving up, the safety of the whole system. And it is a whole system.
Changing course, The difference between the .338 Lapua and the .338 Win Mag is that you use different powders. The ideal powder for a chambering is one where the case is full of powder, the pressures developed at the peak are safe, and the pressure drops to the level of bullet friction as the bullet exists the barrel. Unobtainable, with the powders we have today, and a reasonable barrel length.
If you could have a powder tailored for you rifle, which would include multiple factors, you might approach the .338 Lapua performance, esp. if it the Lapua had to rely on available powders. But you can't get such a powder.
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No hunting rifle can compete with a full-blown benchrest rifle. Pick one.
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They shoot 1,000 yard benchrest matches in Pella, Iowa. Take a trip down there, watch a match, and talk to people. You will get some opinions regurgitated from the "what some guy said" channel, but you will also get a lot of useful information on long-range accuracy performance, and see what benchrest is about.
FWIW