I own all three....
(three Dave? He asked about two...)
I have trade guns, I have full sized Bess..., and I have ...wait for it...., a Serjeant's Carbine in a smaller caliber than the full sized Bess..., not to be confused with Pedersoli's carbine, which is the same caliber as the Bess.
Depends as some have mentioned, on what you want to do. Hunting, Targets, Living History....,
Trade guns and Bess have large locks, which are very forgiving for new shooters. That means they are likely to have less misfires than say a factory rifle made with a small lock. All are robust and tend to take some punishment in the field.
As far as "kick" is concerned, that's physics..., both have metal butt plates, and while the ball for the Bess is larger than that for a 20 gauge carbine or trade gun, the butt on the Bess is longer and wider and more rounded on the edges in many cases, so the pounds-per-square-inch against your shoulder during recoil is mitigated more. IF you shoot an ounce of shot out of both using the same load, the Bess is actually softer.
What it really comes down to is easy of carry. Trade guns tend to be lighter in weight, and with shorter barrels and wooden instead of steel rammer, there is less leverage against your body when you are standing and shooting. The lighter weight also makes for an easier swing on a flying bird, if you should choose to go for upland game. You can get away with less shot and be successful on turkey or squirrels, which is a cost saving, and that is amplified if you decide to shoot a round of skeet or something.
So really, the trade gun is the choice if there is no Living History situation.
OH and some of the colonies had Bess muskets that they issued to Civilians, so not necessarily a no-no for a civilian to have such... but these would be much older models of the Bess than the Pedersoli.
LD