Willysjeep134- From my experience, The Crosman will be more accurate, because it is a .177. Just as a side note, Crosman owns Benjamin and Sheridan. I think all the barrels are made in house.
As for using an airpistol on a trap line, I'm not sure. Most airpistols generate 3-5 ft. lbs of muzzle energy. I guess, maybe on small animals, like muskrat, if you got real close, and shot the head it may work. Personally, I think you'd be better off with a .22 short out of a single shot pistol or rifle. The CCI cb's are quiet and pack a good punch. Or carry a full size air-rifle (pump or spring).
If you are a tinkerer, then the Crosman 1377 can be juiced up a bit, and converted to a .22 (1322). There are a few web sites that deal with the mods.