I don't really remember the Boston teams of the 80's referred to as a "Big 3" team very often. Bird was the clear leader and then you also had Dennis Johnson on those teams that was an NBA All Star talent as well as others that were major parts of the puzzle.
With the current Boston team you could argue that Rondo is at least as good if not better than some of the other Big 3 members and has been there the entire time as well.
Miami is a true Big 3 situation, they haven't won jack yet though. They may end up like the failed "Big 3" in Houston with Hakeem, Pippen, and Barkley though they are closer to their prime than that group was.
With the Spurs you have 3 players that have won 3 Titles together (as well as being title contenders virtually every year)and have unquestionably been the leaders of the team for a decade. The entire core around them has changed multiple times and even gone back to the future with SJax this year but the Big 3 are the constant. Bruce Bowen is the only guy that is even close to being a part of the core but obviously he has been retired for a few years now and the Spurs are still rolling.