Night Hawk. I'm not sure how big the "big-game" is that you're hunting, but I used 200 gr. woodleigh partition in my 308 for african big-game (500 lb to 800 lb antelopes/zebra). They worked great even at 300 yards. The 180 grain suggestion is also very good advice. You may have to special order the 200 grain from a company like Superior Ammo.

regards
Ant