Heavy barrel:

Con - it is heavy (duh).

Pro's - is stiffer ... harmonics are less dramatic, absorbs more of the energy of the acceleration of the bullet .... less kick all else equal due to that Newton momentum thingy we had in HS science, and the barrel will not heat up as fast ... more mass to heat up. Heat is a long range accuracy killer when shooting round after round in short order.

If you are hiking a bunch and taking only a shot or two at a time, a standard barrel will do fine. If you can tote an extra 2# or so, the "heavy barrel" should be no big deal.