Years ago I had an old J Stevens double 12 with a weak hammer spring on the right side. It would virtually always fire a WW shell but was apt to misfire with a R/P shells. It never missed in the left barrel. I fixed it by replacing the hammer spring. It is noted that when it did snap I could break the gun open & re cock & try again & it would fire on the 2nd try. I do not believe that moving the same shell from one side to the other tells you much of anything because the primer has already been dented to some extent & is thus now more sensitive. If with the same lot of shells it habitually doesn't fire in the right barrel but never misses in the left barrel, using a fresh shell for each try, then you can say the problem is with the gun, not the shells.
