Actually, the 6.5x57 was never adopted by any country as a military cartridge. The Swedes and Norweigans used, as you said, the 6.5x55. The Belgians and Serbians the 6.5x53R, the Greeks the 6.5x54, the Italians the 6.5x52, the Japanese the 6.5x50SR and the Portuguese the 6.5x58. No country wanted a cartridge a potential enemy's rifle would chamber, although the Serbians could certainly shoot the Italian's Carcano ammo, until the Italians started using steel jackets.
I suppose every nation figured the 6.5x57, having originated in Germany would be a runaway best seller. The cartridge, as you said, uses virtually the same loads as the 6.5x55.
The 6.5x57 was primarily chambered in commercial, sporting Mausers. The popular wildcat 6.5-.257, which was used in the Arisaka war surplus rifles, differs from the Mauser cartridge only in the shoulder angle and location. Load can be interchanged between them.
The Portuguese, darn 'em, rebuilt their 6.5s into 7.62 Nato standards instead of adopting a different rifle, so I never had one of the 6.5x58s, although some were used in the Portuguese African colonies. Pretty much the same performance. Also the .256 Newton, using a shortened .30-06 case is similar in performance.
