[Brian]

IMO, one needs to take this case by case. Early on, I had most of my cards graded by Baker at GAI.
Several years ago, I took a bunch of GAI graded 1915 CJs over to SGC because I though they were harshly graded (by Baker himself). One did not cross over for the minimum requested grade, but three others crossed to the same grade and two received two whole grades above the GAI grade (they went from 4s to 6s). I think Baker was a strict grader, and at some point, I will cross the others over because of the stigma others allude to. But I may not; I know that they were graded fairly to harshly, not overly generously, and I personally think the card matters more than the holder.
Brian.