8x57 or .308 Win or 8MM-06
To add more options in 8MM versus .308 Win the 8x57 can also be rechambered to 8MM-06. This was a fairly common conversion to use surlpus bolt action rifles, with the use of a chamber reamer and keeping the original barrel, for hunting since the case is merely a 30-06 with the neck expanded. And of course using late date USGI 06 brass also means you are not dealing with corrosive Berdan primers. That being said the next option is still to review the ballistics for each cartridge with a given bullet weight. Then decide what you are seeking in terms of preformance from the rifle and chose accordingly.