Some intercomments by Ron Spomer in his discussion on the 308 in video below.
The cartridge itself is probably the least important part of an accuracy package. Good quality barrel, put onto a well made rifle, shooting good bullets with a consistent load that is tuned to the rifle is key to accuracy.
I think that high pressure rounds are often less tolerant than lower pressure rounds. Nothing per se to back it up, other than my own experience and observations.
Where the 7x57 gained its reputation for accuracy was 100 years ago when it was being compared Martini Henry’s, early lee enfields etc in the Boer War. More importantly it was being used in good Mauser rifles by riflemen who had grown up shooting rifles. If you had given the Boers 303’s they would have a long standing reputation for accuracy.
Today 7mm-08, 308, 6.5 CM are all considered accurate cartridges because you can by well put together accurate rifles and plenty of choice of good well made ammo.
By comparison there are fewer 7x57 being made, many that are available are often well used, abused or cared for, and ammo choice is more limited.
But what I can say is my 7x57 Rigby will shoot nice tight groups with Fox, Remington, RWS, Federal and Hornady ammo - all well within the magic MOA, and more importantly at 100 yds pretty much puts them all to the same point of aim, regardless of bullet weight.
Is that special for the 7x57 - no. I know of other rifles in different calibres that are the same.
@Edinburgh Rifles has a 308 Tikka T3 thats the same, and
@Pine Marten will say the same about his 7-08.
Where the 7x57 possibly has an edge over the 7-08 is you are generally using a longer action with a longer magazine so depending on you barrel throat you can use a longer thus ballistically more efficient bullet with sufficient powder volume to give good velocity. This will be less effected by wind, and thus more forgiving if you don’t read the wind correctly on longer range shots.
The flip side is that 7-08 is loaded to full pressures and thus high velocities from the start. Whereas a lot of 7x57 - especially of US manufacture is loaded on the basis it could be used in 100 plus year old rifles.