Mike,
I too like the ruggedness of a fixed power scope. Yes, I own quite a number of variables, by a variety of manufacturers, but typically even those variables seldom get set higher than 4x, and often at 3x for 90+% of my hunting needs.
Something to consider as well is the light transmission factor of both scopes. Hunting thick woods limits available light at any time of day, and evening and daybreak are critical when hunting the deep woods, when light is even more scarce. I would wager to say that when you compare the two scopes for light transmisson, the 4x Burris will have a greater brightness than does that variable Leupold 1x4, if for no other reason than the size of the objective lenses.
I'll go for brightness of scope over magnification or field of view in your woods hunting situation.
Of course, this is just my very biased opinion, to take it for what it is, or isn't worth.
God Bless,
Marshall