For long range hunting, it's a fairly easy call. I you reload, you want the 7x57 Mauser. If you do not reload, you want the 7mm-08. If you live in Europe, you might want the 7x57 on both counts, but I might step up to 7x64 Brenneke if I lived in Europe.
Sako makes good 5x57 rifles in the Model 85. The CZ 550 is currently produced for the European market in 7x57. CZ-USA has recently imported a limited production run of CZ-550 rifles in 7x57 with the new American stock in walnut only. I got one of those, it came with scope rings, and the walnut had quite a bit of figure, almost looks like a custom stock. Right out of the box with no mods, it's shooting 1/2" groups @ 100 with 150-grain Norma ammo (new old stock for $30/box), the hottest 7x57 factory ammo I could find. 2756 FPS, 2530 FPE.
I had my gunsmith order the rifle, and it was only $697 delivered, total cost. Not bad for a gun that shoots as well as a custom rifle
and looks almost as good. The magazine box has plenty of room to load A-Max bullets as the action is .30-06 size. It has a nice recoil pad, and I could shoot this rifle all afternoon with no monkey shoulder from the recoil. I bought the Norma ammo partly to get the brass, as Norma 7x57 brass alone is over $1 each even in large quantity.
RWS is loading some 7x57 rounds with very advanced bullets, but I think the old Norma SP bullets still have a higher BC. New Norma 7x57 loading is only in the Oryx bullet, for taking tough game at short/medium range as is usually the case in Scandinavia and Africa. Hornady backed way off from their Light Magnum 7x57 loads in their Superformance loadings, and can't match RWS or Norma in energy. If you handload, you should be able to get Norma and RWS energy with a vast range of 7mm bullets. I'll keep my eye out for any Hornady LM loads that might be gathering dust on dealer shelves.
The CZ 550 is also available in 7x64 Brenneke, and if I was going strictly for long range, I would try to get one of those rifles out of Europe or you can buy the CZ 550 action for a custom buildup. But I went for versatility, and if you can reload the 7x57 is more versatile than the 7mm-08 for the extra powder capacity and longer neck, not to mention the rifles come with fast twist to handle the longest bullets. Your chances of getting a standard production 7mm-08 from an American manufacturer that matches a CZ 550 for accuracy is rather slim. I have 4 CZ rifles and what they all share in common is their nail driving accuracy out of the box when you find a good load. A 7mm-08 is a short action and will weigh about a pound less than a CZ 550 7x57, but the slight extra weight is what makes them a lower recoil, long range rifle. Also, the 24" barrel vs. the 22" barrels commonly found on 7mm-08. The 7x57 needs at least 24" barrel to reach full potential. If you want a light mountain rifle, the 7mm-08 gets the nod.
Note: some have complained about the new CZ 550 American stock, but I like it better than the older designs I have handled. The Sako 85 tends to have barrels too short to suit me, but they are lighter weight than the CZ 550. You NEED that 24" barrel if slinging heavy lead long distances.