In your choice of 25 /06 or a 280 or 280 Ai your kind of doing the apples/oranges thing. In 25/06 you are looking at a .257" bullet range from 85gr to 120gr bullet. I don't know where you hunt or what you hunt, but you have a much larger range of bullet weight with the .280 / 284" 7mm bullet. We are looking at a range of bullet weight from 120gr up to 175gr. I have a Weatherby Mark V UL in 280 Rem/ 284" / 7mm that loves 140gr Accu Bonds sitting on top of 54gr of Reloader 19. (sub MOA 3 shot 100yd groups) I recently purchased a Kimber Montana in .280 AI. Why? Damned if I know. I have worked up some loads for it, but have not had a chance to go to the range. If you chose to go with the 280 AI I hope that you reload. Get some Nosler brass, and try a variety of loads. The 280 AI tailor made's are pretty pricey. Keep in mine that these light weights are mint as hunting rifles, not bench rest guns. To add to your search, don't rule out the Tikka T3x, my son has one in .270 Win and he uses tailor made Hornady 130gr SST Superformance rounds, and most of his deer kills are DRT. Good luck in finding the right rifle that meats your needs. P.S. It is heavy but the Win Extreme Weather is a fine rifle.
