A good quality 50 mm objective will give you a marginal advantage in low light, but tends to have a slight disadvantage in weight and price. Because you asked, I just did a side-by-side comparison with two scopes set at the same 16X, one with 40 mm obj and one with 50 mm, peering into the darkest shadows of a wooded patch 350 yards away. The 50mm wins for brightness, but the impromtu test has a major flaw... One of the scopes is a 750 dollar Burris and the other is a 79 dollar Tasco.
In the end, I think optical quality - overall brightness and clarity matter more than objective size. For a hunting rifle, you'll do fine with a 40 mm objective. The only reason I have the 50 mm scope is for whatever margins it gives me hunting coyotes by moonlight, on snow covered ground.