Either cartridge is an excellent choice for the majority of North American big game hunting, and either will do double duty as a varmint cartridge when loaded with light bullets. But the bargain basement rifle market is a race to the bottom. I would gently persuade you to consider a quality used rifle, possibly one from Tradex, rather than one of these new wonder guns if your budget is modest. As for accuracy, well IMHO, we're talking about a big game rifle not a match rifle, so there's more to it than accuracy alone. And while accuracy is nice, we tend to overplay its importance in the big game rifle, sort of a "measure it with a micrometer and cut it with an axe" analogy. How the rifle handles and balances is far more important than the question of fractions of a minute of angle of accuracy. One important aspect of a hunting rifle for me is whether I can run the bolt with the rifle at the shoulder. Some of these inexpensive rifles have pretty stiff bolt lifts. Another aspect to consider is the ease by which the stock can be made to fit you. Many inexpensive plastic stocks are cut too long for the average guy, so if you need to knock an inch off the LOP, can it be done quickly and inexpensively? If the stock is hollow plastic, you might find that's a problem that threatens to increase the cost of your rifle. If you decide to use the rifle as it comes and its too long for you, the butt will catch on your clothing as you shoulder it, recoil will feel a bit worse than it really is, and it may be difficult to acquire the correct eye relief to your scope.