Either is a fine choice. Essentially you get about another 100yards of range from the 257, with more flash bang. Ammo costs are lower and generally more available for the 25-06. You'd probably want a min. 24" tube, 26" probably better on the 257, where the 25-06 works well in a 22", with 24" probably better. Recoil is moderate with either, more a function of stock design and rifle weight, but if all is equal, 257 will give a bit more. I shoot a 25-06 often for deer and antelope and do not hesitate to use it on cow elk. It has taken game cleanly to over 400 yards, with the capability to go further. For me, I'd pick the 25-06 as I would not shoot one further than the other. When I want ultra long range, over 400, I step up to a 6.5mm to 7mm with at least 140-168 grains to keep energy
up. But if you want to reach way out there with a 25 caliber, the 257 will give you more reach and become the better choice, IMO, for that sort of work. No wrong choice.