This is just an opinion here because I don't have experience yet shooting or hunting with a swamped barrel, but my hunch is that the swamping becomes more of an advantage with longer rifles.
For instance, I refer to my Lyman TR as a carbine because it is so short. The barrel is straight and I have no problems shooting it off hand. I notice that when you step up to the Lyman GPR, it feels much more muzzle heavy. I believe in the old days when longrifles with barrels >40" were common, the swamping helped reduce excess weight from the long barrel.
Of course, the muzzle weight of a rifle is strictly a matter of personal preference. Some like a lot of weight up front for shooting off hand, while others like myself prefer a more balanced feel. When I shoot off hand, I place my left hand very close to me, just in front of the lock. That tends to add more weight to the muzzle, so that is why I prefer a gun without the extra muzzle weight to begin with.
Of course then there is the whole issue of style with regard to a swamped barrel. I also like a swamped longrifle because it is more in line with the originals.