I haven't heard of the "new" way and my car is old. So "old" way it is. Farthest first.
And for what its worth I do farthest first on all my newer vehicles too.
Regardless, if you look into the physics of the process the only way air is introduced into a sealed system is through the respective front or rear reservoir or an open brake line. If you let the reservoir go empty then you're starting again. If you temporarily remove one front caliper to replace it opening up a line, you'll only have to bleed that side. Unless the line is open long enough for all the fluid to drain out back to the nearest T, which is highly unlikely. But if it happens then both sides that are effected need to be done.
