I have a 300 WinMag. Before I ported the Barrel it was a killer. now the felt recoil is like my .25-06. I really enjoy shooting it now. I know this might disagree with what the other guys are writing, but I keep it in my truck and its kind of my go-to gun when my .22LR isn't enough. seems crazy to go that big but its comfortable to shoot and its an older Winchester model 70 with a 2# trigger that has been scratched up and I am not trying to keep it nice anymore. It was my first High power as well which is why I am so comfortable with it.
Having said all that, I have laid down whitetails at 500 yards with it that have never gotten back up. as most people say, its about shot placement at extreme distances. so the 308 at 1000 yards would probably be to small for a good clean kill but I wouldn't want to get hit with one at that distance, especially in the chest! (165 grain bullet @ 2800FPS MV has 700 Ft# energy at 1000 yards). With a 300 WinMag a 200 grain bullet with a muzzle velocity of 2900fps, you still have just over 900 Ft Pounds of Energy left at 1000 yards. If you can push a 220 grain bullet 3000FPS with the RUM you will get just over 1000 Ft# of Energy @ 1000 yards. Just for reference, a 243 can easily kill a deer at 500 yards with good shot placement. 100 grain bullet with MZ of 3000FPS yields 1052 Ft# of Energy. I would say that is more than adequate power if you are good with your rifle. So if you want to kill an elk at 1000 yards (how many of those shots will you make in your life?), you would probably be better off with the RUM, but if you are going to stay within 800, the win mag would be IMHO, more than enough. Of course, like with most issues on this forum, it boils down to personal preference...