I sort of agree with razormatt in that I see three distinct options:
1. Go smaller, a lot smaller, like a .243 Win, 6mm Rem, .260 Rem or 25-06. Or really smaller
like a .204 Ruger, .223 Rem or 22-250 for varmints only. Cheaper to load and shoot, no
recoil and amazing accuracy potential in a tuned heavy barrel rig.
2. Go bigger, .325WSM, .338 Win Mag, .375 H&H. Prove that you have testosterone! Rattle
your teeth with each shot. Invite osteoarthritis as you get older.
3. Go frugal. Stay with the same bore size, use the same bullets and primers for both rifles.
Smaller option .308 Win. Potentially improved accuracy, cheaper to load (less powder per
round), reduced recoil. Can be had in short handy rifles. Bigger options .300WSM, (nice
short action, potentially more accurate, increased power, without overwhelming recoil),
.300 Win. Mag, slightly more power potential, improved long range performance, .300
Weatherby or Remington Ultra Mag (see option 2 above).
Were it me, I would look hard at the .300WSM in option 3. I am cheap, so using common bullets and primers, maybe even powder, (4350's work well in both, H-414, too from what I hear). Nice short action, increased power without kicking me to death. Sort of dovetails with my future plan of adding a .270 Win to my tiny battery, which currently consists of a .270WSM and a 6.5x55 Swede. Common bullets and powders keep inventory at manageable levels which annoys my wife less, still provides good performance on big game. Probably a better varmint cartridge than my 6.5x55 with its' accursed SAAMI spec long throat. It can't shoot lightweight varmint bullets to save its' life, to my dismay.
Anyway, that's one way to look at it. Be sure to let us know which way you decide to go.