25-06 Remington
Only covering the animals you listed I would go with the 25-06. If you were to want to hunt Elk I would then choose the 270. Even Wal-Mart at least in my area has 25-06 ammo in the Remington Core-Lokt. I would use 110-120 gr. ammo on deer & hogs and use the 85 gr. loads available on varmints. I love the 25-06 and have used one for many years. I handload but if you don't there are loads for the 06 that cover all the animals you listed. If you want one load for everything you could go with the 100 gr. Barnes TSX loaded by Federal if your rifle shoots the load well enough. In the end you can't really go wrong with either caliber but there aren't any varmint loads available in factory ammo for the 270 that I'm aware of.