While there is nothing wrong with the Lee Enfield, the Weatherby vanguard is objectively the better hunting rifle. It will have a better trigger, be lighter, cheaper to feed, more accurate, stronger, and less worn. The Enfield has a greater magazine capacity and a faster action, both of which pertain more to the battlefield than big game.
Of course, the Enfield will be significantly cheaper than a new or even used Vanguard, yet you may find yourself wishing to upgrade after a season or two. If you're looking for a more "classic" rifle at an affordable price, a used Husqvarna may be attractive. This will be cheaper than the vanguard, yet far more appropriate a rifle than a Lee Enfield.
Although the Vanguard is the rational option, that doesn't make it the better of the two. Ultimately you are choosing a rifle to bring home meat with, and if we were entirely rational we may choose to go to the store instead. Pick whichever rifle you like the best, and I'm sure you'll have made the right decision.