If the available choices include .280 Rem or 280AI; I'd seriously consider that. Excellent accuracy and distance with a 7mm, but not
all the recoil of a 7Mag.
My experience was limited and some time ago; but I found the 280 Rem to be very accurate with less recoil than the 30-06. It was also quite easy to develop accuracy handloading with Nosler 120, 140, and 150gr bullets. 160's would have been next, but my Brother took his back, so I don't have anything current to share.
Good factory ammo is available for both, and the 280 can be fired in the 280AI, it simply fire forms to the AI's chamber. I suggest this
factory rifle. I had the opportunity to work with pair of Ruger 77 MKI's; a Sporter, and a Varmint model. They were the most satisfying rifles I've ever had the opportunity to use.
My current LR chambering is 260, and it's a true peach; but my Large Game hunting experience with it is zilch; Deer, sure I would, Elk, probably not for me.
I've become enamored with the Speer Gold Dot bullets. They could be an answer I've been looking for; a bullet with match grade accuracy and very capable terminal performance in the single package. I am very early on with handloading projects dealing with this. I'll be working with 223 62 & 75gr, 6.5Grendel 120gr, 260 140gr, 308 and 30-06 168gr.
I do the bulk of my large game hunting (deer) with 30-06, I have no complaints; and I've not really had much opportunity for LR Big Game hunting.
Greg