The 18th at BB is one of the worst finishing holes I've ever seen, let alone of a major championship course. It would seem that both holes are far from the best closer for a US Open, though the finish at BR seems better of the two by default since BB 18 is so bad.
Of the finishing holes Bill mentioned, they are all far better than the finish at BB and are major league holes compared to BB, which is a single A hole (no pun intended).
For me, probably at no surprise, the best finishing hole on major championship courses is Merion East. It has to be the hardest to par or birdie of them all so in that regard it is much different than the rewards possible from TOC 18 or PB as a par 5 in the modern world. Carnoustie is as difficult to par as Merion because it easier to one-putt and avoid a three-putt for that matter. So Carnoustie is an easier bogey hole, though the last couple of Opens would have one think otherwise. It was simply bad decision making in one instance and bad execution in another.
If one accepts the final hole as being a difficult one, and I do, then Merion's 18th is all one can handle. It has length, an imposing tee shot, a rolling and canted fairway, an upslope and false front green that is crowned along the line of play. It has a wide opening for a run-up opportunity, but that has to be precisely executed or else the ball comes up short in the back to front sloping portion of the first half of the green or runs over the green in the front to back sloping portion of the rear half of the green. There are no bunkers on the tee shot, just as well given the high demand, but the bunkers at the green end are deep and threatening.