Does your state have a minimum barrel length for handgun hunting? If not, then the choice is yours. With the power in a .500 S&W mag, I doubt that the little bit of lost velocity of a 4'' barrel is gonna make much of a difference. What will be obvious tho is the increase in amount of felt recoil. The term ''half-lug'' just means the lower part of the barrel(in which the extractor rod sits in) only goes halfway, as opposed to a full lug barrel, which extends out to the end of the barrel. Some folks prefer one to the other mainly on aesthetics and balance. Full lug barrels sometimes help with felt recoil and barrel rise because they add weight to the gun and put more weight forward.