I didn't hear what Sam said after the match, but the advantage of waiting until half time to change things must be that it denies the opposition the opportunity to respond by making a change of their own, at least to some extent.

Of course, it's possible to change during the passage of play, but there has to be an advantage to having the coach stood in front of the players, with their full attention, explaining to them exactly what changes he wants to make, and how he wants each one of them to adjust their game.

Doing that at half time denied Bruce the opportunity to do the same with his players.