I have both, and it is an obsession. The .308 is a tough shot @ 1000 yards if there is any wind. It can and is done all the time, but I would say that more than likely you will find yourself inside of 1000 yards and not going home frustrated. Also, you will NOT be $200.00 lighter in the wallet while winging .308 lead out to 1000 yards and having it get pushed all over the place. It has taken me a year of shooting every other weekend to hit the 1000 yard steel target at my range 3 times in a row for a verified 18" group in 15 mile an hour winds and an 11 degree uphill angled shot. I have hit the target many times, but never was able to back up the shot. last weekend during a 5 shot string, I hit the first shot, missed the 2nd and hit the next 3 in a row. 4 shots, 1000 yards, uphill and just under 18" group on a 36" steel target. It was a really good day for me. I have been shooting long range (beyond 400 yards) with a bolt gun for almost exactly a year. I don't hunt.
If you do it in steps, I would suggest going with the .308 at first, and NOT spending the extra money on a 5R, but rather getting one of the more affordable flavors with a 24" barrel, honing your skills between 600 and 800 yards, then send the barreled action off to Chad and John @ Long Rifles and having it trued up and hang a 6CM barrel on it and start shooting beyond 800, 1000, and even 1200 yards. The 6CM is a .243 parent case so no need for a new action, and if you get a barrel vise and action wrench, you can do a switch barrel set up and swap it back out to .308 right in the parking lot at the range. Yes the 6CM is a "wildcat" cartridge from what I gather, but it is reported to be a laser pointer when properly set up.
My next barrel purchase will be a 6CM and I plan on using one of my .308's as a donor.
Good luck with your decision brother. I am a newb, and NOT a guy with a crap load of experience, but I have spent a crap load of money going after the 1000 yard game, and this is what I have learned so far. My mission is to shrink that 1000 yard group down under 10" before the summer is out. I shoot Hornady 178 AMAX, 178 BTHP and Nosler 175 BTHP. I also have hit the 1000 yard steel with 155 Scenars a few times. I can pepper ALL of the steel 800 yards and in with 155 Matchkings (and all of the bullets listed) at will. It truly is an obsession.......... for me.