The best cut of pork for pulled pork sandwiches is Boston Butt. The pork shoulder is usually cut into 2 pieces, one of them being the picnic and the other the butt or Boston butt as it is commonly known.
The picnic can be used but does not have the fat content that the butt has. The fat is what keeps the meat juicy all the way through during its long time in the smoker.
A lot of the fat melts away during the cook time and if you cook it properly, it will yield some of the best pulled pork you ever ate.
Rub/Massage all over with your favorite rub and make sure to get it into every nook and cranny and let it sit while you get the smoker ready.
Smoke fairly heavy with mesquite or your favorite wood until the internal temperature of the meat reaches about 145-150 degrees.
Then wrap in heavy-duty foil and continue to cook it until it reaches 200-205 degrees.
When it reaches 200 degrees, remove it from the heat, wrap in a thick towel and place in a cooler for about 2 hours.
Once you open the foil, it will literally fall apart and a little stirring is all that is required. The meat will melt in your mouth.
You can pull it just as soon as it reaches 200-205 but it will not be as tender that way.