Nice looking chair! This is an area where I'm really quite ignorant, actually. What are the essential differences between the two types of Burke?
The only difference is that that the Burke 116 chairs have raised "arms," while he 115s don't. You can see the difference between the two types of chairs in this shot from "The Conscicence of the King:"
Kirk always sat it a 116 in the briefing room while all the other chairs were 115s. Kirk also had a 116 in his quarters, and McCoy had one at his office desk. All in all, the 116s were a tiny bit "fancier" than the 115s, and they were used in all the places where you might want a slightly fancier chair--like "taking the stand" chair in legal proceedings.