Either rifle would be fine. There is an advantage with the .308 with heavier bullets and also if you and your ammo were to be seperated during travel over, you are probably not going to readily find any 270 WSM ammo anywhere.
Pick a good bonded bullet of your choice, i.e. Nosler Partition, Swift A-Frame, Barnes TTSX, and see how they shoot in your rifle. I would stay on the heavier scale for each caliber 150 for the 270 and 180 for the 308. Once you find the right combination that shoots well, practice, practice and more practice off of shooting sticks.
Also practice shooting sitting and from other postions and the sticks at different ranges. This sounds a bit odd but jog in place for a few minutes, empty handed of course, to get your heart and breathing rate increased, similar to the excitement of a long stalk on an animal and practice shooting from different positions. Hope this helps.