Though I am only up to one briar at the moment, I already know the answer to this question for me.
Always keep the sock. Only keep the box if the pipe is particularly nice/special/fancy AND the box is also a quality box. It isn't about keeping value or something by having the original box (I think most buying estates or used pipes wouldn't care), but more about if I moved or something, I have a place to put the pipe to be protected. It's purely practical.
But when I say only if it's particularly special/etc, what I really mean is more, "did this pipe cost $500-1,000 or is it just $50-150?", or is it a situation with a "certificate of authenticity because it's a limited/special edition and numbered" thing.
Otherwise, a box is just clutter and I'm not a particularly sentimental kind of person.