Glad you narrowed it to Hawkens, because I can be the most help there. I've got a couple of them, both 58 caliber- one with a 36" barrel tapered 1 1/8" to 1" and the other a 26" barrel tapered 1 1/8" to 15/16". I also have three 58's with 1" straight barrels- two with 28" and one a 32" straight.
Here goes the subjective stuff. The one with the 26" taper actually weighs more than the 28" straights. But it feels absolutely "whippy" when you mount and swing it, more like a modern upland shotgun with the COG right between your hands. The rifle with the 36" taper weighs a whopping 12 pounds, yet balances better for my tastes with a little less muzzle weight than the 32" straight weighing 3 pounds less. The 28" straights feel like they have a little less muzzle weight than a 50 cal Lyman GPR with its 15/16" barrel if that's a useful comparison, and they weigh a little less, too. Overall they feel quicker or more lively, whatever you want to call it, due both to the lighter overall weight and less muzzle weight.
Lotta comparisons to ponder, but overall the taper really improves the Hawken handling for my tastes, though retaining a little more muzzle weight than the swamped barrels I've handled. I've got longrifles with 39" and 42" straight barrels, and they all feel to me like they "need" swamps. I'm not sure I'd like as radical weight shift as a swamp on a Hawken if such a thing was made. That 26" 58 cal with the radical taper is reminiscent of a swamp feel-wise.... A dandy for quick field shooting, but it's an absolute stinker for deliberate offhand shooting typical of small game shooting with a smaller caliber gun.