Just for reference, my 12g 26" BSS is 7lbs 8oz. It has a relatively slow swing weight due to the heavy walled barrels which are common to all BSS guns, 12g and 20g alike.
My two 20g BSS guns are both 6lbs 8oz. One is a pistolgrip 28" bbl and the other a straight stocked 26" bbl.
I can highly recommend the 20g BSS in either configuration for an upland gun. If you're looking for a waterfowler, the 28" or 30" 12g may be for you. Otherwise, the 12g BSS in any barrel length or stock config is a bit heavy for my tastes, even though I hunted my 12g for many yrs of upland. My 28" F/M choked 20g with 1oz Rem Nitro Phez #5 shot swatted SoDak wild phez out of the sky this last October just like a 12g.