Daryl, this is what the 1940 RWS table says, all velocities from a 60 cm barrel:
:
6.5x54 M-S, bullet 10.3 gramm H-Mantel hollow point , pressure 3200 atm, 760 m/sec
6.5x57, 10 gramm H-Mantel hp, pressure 3200 atm, 742 m/s
6.5x57R, 10 g H-M hp, 2900 atm, 731 m/s

6.5x54 M-S, 10.3 g rn, 3100 atm, 756 m/s
6.5x57, 10 g rn, 2900 atm, 684 m/s (R the same)

BTW, the CIP max pressures of European metric cartridges were never based on destruction tests. Instead, the go back to the 1940 German proof law. Handloading of smokeless rifle cartridges was then virtually unknown here. The purpose of the law was to make sure that any custom made rifle should be safe with any factory load then available. So each gun was to be proofed for the highest pressure load of that cartridge then available from the German factories. This pressure was set as the future maximum for each cartridge, to make sure that any gun chambered for a given cartridge would be safe with any future factory load available. From the same time all factory ammunition lots are to be pressure tested at a proofhouse. This rule "highest pressure of a 1940 German factory load = maximum pressure for that cartridge" results in the puzzling differences in max pressures, though the cartridges may be on the same basic case and are usually fired from rifles of the same designs. Take for instance the CIP max pressures for the four Mannlicher-Schoenauer cartidges, all used in rifles of the same construction: 6.5x54 = 3650 bar (electric transducer), 8x56 = 3200 bar (et), 9x56 = 2400 bar (copper crusher), 9.5x57 = 3050 bar (et). The British "tons per square inch" were likewise converted to CIP bar, disregarding the completely different and more inert Woolwich pressure testing setup, which gave only about 80% of the Rodman copper crusher readout . This too leads to puzzling results. F.i., all pre-WW2 ".275 Rigby" rifles were made and proofed in Germany as "7x57". But now the 7x57 has a max CIP pressure of 3900 bar, while the .275 H.V. Rigby is listed with merely 3200 bar. Or, take a look at the .404 Jeffery and the .416 Rigby: Prewar British data lists the .404 with 16 tons, while the .416 was 17 tons. The CIP numbers now are the other way around, 3650 bar for the .404 and 3250 bar for the .416! Reason here: Other than the .416, the .404 was loaded in prewar times by DWM. DWM used other powders than the British Cordite and, most important here, had both it's own and Kynoch loads pressure tested with the more sensitive Rodman type copper crusher equipment. DWM loads certainly did not exceed actual Cordite pressures, but the equipment readout was different. So CIP accepted the DWM numbers as standard maximum on the .404, while other tons per square inch readouts were merely converted by calculator to bar.