ORIGINAL: Pavomesa
A lot of tests have shown the notion of "brush guns" is pretty much a myth. Light fast bullets tend to explode in brush. Heavier bullets get deflected. As for killing your game, one is about as bad as the other. Your situation probably depends on how far your shots are and what you might meet in the woods. Thick brush isn't great hunting ground for anything and I suspect you hunt the open spots where your 270 is fine. A 30/06 isn't terribly different from a 270 but it will give you a heck of a range of bullets to choose from and it shoots them all well. The 30 magnums only give you more of what you already don't need...more velocity to blow up bullets when they hit brush.
If you want to get into the woods and play jungle warfare, a 30/30 would be as good as anything.
The above is 100% accurate! If you want something a little different, get a BLR in .358 Winchester. It is no better if it has to shoot thru twigs and brush, but it makes a big hole so the blood trail is easier to find. In addition, it is a medium-range cartridge that is good all the way from 5 yards to 300.
Personally, I used my .270 Mannlicher/Schoenauer carbine (20" barrel) in the swamps of southside Virginia with absolute satisfaction!