Ebonitekid,
I've got the new (2007) .44 mag H&R, and am very happy with it. Got my first deer with it on Saturday. Wasn't a difficult shot, but was a nice clean kill with large entry and exit wounds. I've never shot the .444, so I can't compare the two. Plain old factory ammo (240 grain Winchester Super-X jacketed soft points) is shooting 3.5 inch groups at 100 yards in my .44 mag. Hornady's factory ammo was more accurate (a little less than 3 inch groups) but more expensive. I got a good deal on a large quantity of the Winchester's, so I used them for practice to familiarize myself with the gun, and stuck with them for deer season.
The best thing I ever did for myself for hunting brushy woods was to purchase a low-power scope (2x Leupold shotgun scope). It brings all those pesky little branches into focus, and really helps me thread the bullet through the brush. My eyes have reached the age (50) where a brown deer in brown brush aligned with a brown-black post and blade turns into 1 brown blur. Everyone touts the quick target acquisition of open sights. I have found that if I keep the magnification low and shoot with both eyes open, the scope comes on target just as quickly, and I have a LOT more confidence in taking the shot.
Duane