I'd seriously look into a 3-9X40 instead, especially on a budget. You'll get better quality for half the money. I'd take a high quality 3-9X40 over a cheap 4-14x50 any day. Especially on a heavy recoiling rifle. And a 4-14X50 of the same quality will be twice as much money. Another thing to consider, the heavier the scope, and the higher it is mounted magnify the effects of recoil. A 338's recoil is going to be harder on bigger heavier scopes. Those scopes are designed for low recoiling varmint rifles.
A 14X scope is meant for varmint hunters who need to hit small targets at 400-500 yards or target shooting, not big game hunting. A scope on 9X is enough magnification to hit any big game animal out to at least 700 yards.
In theory a 50mm lense is better in low light, but not usually in practice. The scopes magnification combined with objective size determine the diameter of a beam of light that exits the rear objective to the eye. Simply divide the objective size by the magnification. A 50mm scope set on 10X lets in a 5mm diameter beam of light. For most human eyes 5mm is as much as can used. If it is less than 5mm then the scope will not work well in poor light. Greater than 5mm rarely helps since it is wasted light the human eye can't use.
A 40mm scope set on 8X lets in exactly the same amount of light as a 50mm scope set on 10X. At any magnification less than 8X or 10X both scopes provide more light than the human eye can use. Above 8X or 10X both scopes perform poorly in low light. So for double the money a 50mm scope works slightly better than a 40mm scope, but only when set on 9X. Any more or less magnification and you get the same results.
And that ASSUMES equal quality. If you buy a scope with better quality glass the image will be clearer and sharper even though the beam of light is smaller. At about $200 the Burris FF-II has earned a reputation for ruggedness and decent quality. That is the least expensive scope I'd put on your rifle. For slightly more a Leupold VX-1 should work. You can move up to the $300-$350 VX2 and get a little better quality glass, but the VX1 is just as durable.
