6.5X57mm has long been a popular deerhunting round in continental Europe, especially Germany, for those who wanted a bit more performance than the 6.5X54 M.S. produces. This is partly because 6.5mm cartridges have a much longer history there in this role than in the US going back to the turn of the 18th/19th centuries, and also because many European countries had restrictions on civilian ownership of rifles chambered in 'military cartridges', ruling out equivalent numbers such as 6.5X55mm and 7X57 for most of the last century.
It is a nice cartridge, but doesn't do anything that the 6.5X55 can't do, nor 260 Rem or 6.5mm Creedmoor. It can't do anything either that 7X57mm with decent handloads doesn't do better, although it produces a bit less recoil. As said above, the 257 Roberts (and 6mm Remington for that matter too) are basically the same thing taken down two more calibre steps. The 257 seems to be one of those 'happy' combinations that work exceptionally well, better than the paper specification would suggest.
If a modern and/or well-built 7X57mm rifle - and we still don't know what make, vintage or type produced this question - can't better 1.5" 100 yard (assumptions again!) groups then there's a problem with the rifle not the cartridge. The old Mauser shoots very well in a good rifle, and amazingly well in 100 year old Mauser service rifles. I owned a long DWM M1895 Boer War (1898-1902) souvenir rifle many years ago that externally was not a looker (and I mean really rough!!!), had a mismatched bolt, but had a good bore and it shot 10-round 2-inch 100 yard groups with handloads shot off the elbows with sling support and through the really basic 'partridge' foresight and simple leaf rear with a tiny V as the sight-form. I currently have two Chilean 7X57 Mausers, a DWM M1895 and Steyr M1912. The latter's first range outing earlier this year to see if it worked and do some load development saw 1.75 to 3-inch groups off the bench with handloads despite my near 70 year old eyes having real difficulty with the crude iron service rifle sights. I also have an early 1950s BSA 'Hunter' deer rifle in the calibre and in original condition with a contemporary 4-10X40 Pecar 'scope (quality German make). It shoots just over the inch with old European factory ammo, but I know that its previous owner's handloads could halve that - which is what I hope to achieve when I get around to doing some loads for it. Although these early post-war Beezers were superbly made, short of getting a one in a thousand example, I wouldn't expect them to match a good modern rifle from Ruger, Savage, Sauer, Tikka and suchlike.
The other factor may of course be ammunition. Frankly I've rarely been impressed by US manufactured metric rounds for older rifles - 6.5X55, 7X57, and 8mm Mauser - from the mainstream companies. They have been downloaded so far in the interests of avoiding problems with old clapped out surplus rifles or weak models that they usually perform very poorly. Some Hornady 140gn PSP 6.5X55 ammo I tried a few years ago in a Savage PTA Based F-Class rifle with a 30-inch Bartlein struggled to better two inches at 100 off the bench. It had such low MVs that a bit of QuickLOAD modelling suggested it likely only produced 35,000 psi, and there was a 120 fps ES from a 5-round string !! If you knew not6hing about the 6.5X55, this experience would have given a completely false impression of the cartridge's abilities. (The rifle shot under a third-MOA, sometimes 5 in 0.15" at 100 with 140gn Berger LR BT handloads.)
the cool thing about it is that just a little work and this factory rifle shoots lights out and cheap!
