The 7X57 (7mm Mauser) has similar ballistics to the 7-08 Rem in many loadings despite having a larger case and using a bit more powder. It is better suited to the heavier bullets above 150gn than the 7-08 in standard short-action guise though. Many loading manual maximum loads are limited to around 40-45,000 psi because of the number of surplus South American M1895 military rifles around with the weaker 'small-ring' Mauser action. SAAMI standards for factory ammo are a modest 51,000 psi MAP. It can be loaded more heavily though for use in modern actions like yours. Brass and dies are easily obtained and like the 30-06, it is a handloader's dream design, very flexible and easy to get good results. Like the 30-06 it has a longer neck than you find on more recent designs. Like the 7-08, it'll perform well in a short barrel - sound moderated (suppressed) short-barrel rifles of 20 inches or less are the norm here in our deerstalking, and many military users in the dim and distant past had short cavalry carbine versions with 18-19 inch barrels as well as short rifles (24").
This is a real piece of history - developed in 1892, first adopted 1893 (Spain) - and used against the USA in the late 19th century Spanish-American war in Cuba and the Philippines and against the British Empire by Boer republic 'Kommandos' in the 1898-1902 South African War, in both cases with the same Mauser rifle design and with devastating results on doughboys and tommies. As a result, it heavily influenced the US Army to drop the 30-40 Krag and adopt the M1903 Springfield. (Britain would have ditched the 303 Lee for a 7mm if World War 1 hadn't started when it did.) The US .30-03 / .30-06 cartridge was heavily influenced by the 7mm Mauser and can be said to to be a 30-calibre descendant of it. It saw widespread use as a general purpose game and self-defence cartridge in Africa for generations and killed much larger, tougher animals than its ballistics said it should - 175gn at around 2,300 fps in those days. Many South American countries used it as their service cartridge until the 7.62 appeared in the late 50s.
Its survival today in everyday sporting use at the age of 126 shows just how good a cartridge it is - capable of great accuracy, and reckoned one of the best ever medium deer cartridges by some authorities. It still has a considerable following in the UK amongst our deerstalkers. Ruger has chambered it in No.1 and M77 rifles at times for the US market. I have a friend with a mint Number 1 he has had from new and will never sell it. It has taken Canadian elk, moose and one large black bear, as well as many British deer and feral goats.
I have three 7X57s (two Chilean long military and one 1950s classic BSA deer rifle), 7mm-08 and 284 Win F-Class rifles. I like them all and they all do a great job when the rifle is properly set up and good handloads produced. I have a real soft-spot for the old Mauser number though.