The 30-06 should do just as well as the .308,
they shoot the same bullets. I have a 30-06 and am starting to get into varmiting also. The 110 gr. Hornady Spire Points shot better in my gun than the 125s, but every gun is different. Both of these larger bullets are kind of destructive so if you want to keep any pelts you may want to get a smaller gun like the .223.