In the Ruger Precision Rifle, I'd recommend the 6.5 Creedmoor over the 308win.
Truth be told, the 308win does win a lot of matches at 600 and 1,000yrds still to this day, but that's largely because there are 600 and 1,000yrd matches that ONLY USE 308win!!! When you look at competitive firing lines around the USA in matches that don't require 308win (i.e. non-PALMA), then you don't see a lot of 308win's at the top. Largely you see 6, 6.5, and 7mm cartridges winning matches. Which is mostly due to the nature of the beast - you're shooting a lot of shots, burning a lot of powder, and taking a beating on your shoulder. You want high speeds and good aerodynamics, with moderate recoil such that you can touch them off fast and frequently without beating loose your teeth. 30caliber rifles aren't famous for that...
30caliber cartridges have to run over 200grns to get ballistic coefficients over 0.6 (G1), whereas the 6.5 Creedmoor will go over 0.6 with a 140grn pill. Considering they're coming out of the same case, the 308win will throw that 0.6 BC 200-220grn pill somewhere around 2400fps, whereas the Creedmoor will push a 140grn bullet with the same aerodynamics (same BC) at 2700fps.
Not to mention, the 308win Ruger Precision Rifle only has a 20" barrel, compared to the 24" tube on the 6.5Creed version - so the gap in muzzle velocity stands taller still in favor of the 6.5Creed.
And of course, the 200grn 2400fps 308win will punch over 25% more felt recoil in the same rifle - BUT - the 6.5 Creed also weighs almost a full pound more than the 308win, since it has a longer barrel and a smaller bore, so the felt recoil on the 6.5Creed will be even further less than the 308win simply because of the rifle weight.
Don't get me wrong, I love the old 308win, and I've done a lot of 1,000yrd shooting with them in the past, but it's just a fact that for targets at long ranges, the 6.5 Creed has real world advantages. Even for hunting, the 6.5Creed is plenty for deer as far as you can hit them, and will flatten elk sized game without issue. I killed a lot of game in college with a 6.5x55 swede that nearly replicates the 6.5Creed, it'll put meat on the table.
Also, the recoil of the 300win mag isn't bad in a 12lb+ rig. If you're shooting a 7-8lb hunting rifle, that's one thing, but you're not talking about that kind of rifle.
In your shoes, I don't think I would buy the RPR. You already own a Remington 700, and whatever scope you have on it. The RPR is going to set you back $1000 for the rifle, then $500-1000 on your scope to ride it, and any ammunition cost on top of that. Neglecting ammo, that's $1500 in your pocket, earmarked for a precision rifle... Put some of that $1500 towards rebarreling and rebuilding your 30-06 and you'd end up with a rifle that's every bit as good as the RPR could ever be. $300 on a shilen barrel, $300-500 on a new stock, $200 on a Jewel trigger, and $500 for a smith to blueprint and put it together, and you've got your $1500 invested into a real precision rifle.
But... That does take away the fun of buying another rifle...