I get a better price buying whole shoulders, so I tend to buy them that way and usually have them cut in half into the two shoulder cuts: butts & picnics.
I can honestly say I have no preference on either cut with one exception; If I'm going to cure one into a ham, then I prefer the picnic cut ONLY because it resembles a true ham.
Here's a picnic ham I did a few weeks ago at the Fall Gathering down near Augusta, GA. Maple Glazed Ham
For pulled pork I use both cuts and as long as they're tender, once pulled I cannot tell any difference.
Whole shoulders have another great advantage; "WOW" factor.
I prefer the Butts for pulled pork. They seems more compact as well. Seems like the Picnics have more connective tissue and collagen to breakdown and seems to take a little longer cooking them. Pure flavor, I think the picnic maybe has a slight "porky" depth of flavor, maybe from the additional connective tissues. Once you put on a bun with sauce or slaw however, I find it hard to notice a huge difference.
Yep, for pulled pork I am convinced it really doesn't matter. I cook both cuts side by side often and honestly can't tell any difference in cooking time, tenderness or taste once pulled (even without sauce and/or slaw).
When I lived in NC, there were some who swore by the butts, some swore by whole shoulders and others swore by whole-hog. They all tasted great.
About four years ago, at a Marching band cookout, I did a blind taste test with all the adults (about 15) to see if anyone could tell any difference between the two cuts once pulled. Absolutely no one could really tell (including myself) and some of them thought I was playing a trick.
I'll be cooking some this Friday for the Band's end of the season party. I'll try and get some pics. I may try the blind taste test again.