The brown strap with brown stitching is the perfect match to the warm rose gold that Breguet use for their cases. Changing to a black strap may pick out the black dial printing a little more, but it will unbalance the watch to my eyes. Yes, the watch 'head' will stand out on your wrist but it's not the harmonious wearing experience that you want from a Breguet. You could go a shade or two darker brown on the strap and see how that works.
But as usual, it is up to you and worth a try. Please report back on how it goes.
Andrew