I've done it both ways, and to me choosing one over the other depends on what has been done to the brake system as both ways have their place.
Typically, with just wanting to change the fluid and nothing else, doing it in way #2 is just fine and dandy.
Doesn't take long.
If I had the brake line disconnected for some reason and had to completely fill the system back up with fluid, I'll start with #1 to get fluid in there, and then finish off with typical bleeding, which is #2.