Ah, but Dr. Rob, I believe the young man is implying that he's using what he's got, and he's spent his pennies on a heavy .308, so that's what he's got. I understand-- I've done it a lot, too. But I've got to agree with Rob that you could do a lot worse than an 870 with slug barrel for brush hunting, if you know all of your shots would be under 100 yds. Used 870s are thick on the ground for under $200, and slug barrels are only about $100, new. So, for around $300, you've effectively increased your armory by the equivilant of 2 guns! Always a worthy investment! If your shots will be under 75 yards, you could shop for a vent-rib 870 and pick up some screw-on open sights like I did from Brownell's for about $35, and you can get reasonable accuracy with those and your original barrel.
Not trying to dissuade you from blooding your Winchester .308, just pointing out that there are options, very reasonably priced. As for effectiveness, all of these options are just fine.