I'd go with the .308 for 2 reasons ...
1. Availability of ammo just about anywhere
2. As aaalaska said, since you already have a .243, the .308 will give you a wider spread of bulllet weight options. The .243 will go from 70 grain balls to 105 grain. And the .308 can cover from 100 grains to 200, with the sweet spot in the middle. Gives you pleanty of spread.

But, if you handload and have an itch for a .284 bore, then get what you want. The 120 grain to 175 grain balls the 7mm/08 wil spit will get your hunting done just fine as well.