I've tried both ways and prefer leaving both inserts in the mouthpiece to catch any drops of liquid where I can see them. Part of the draw feed system in the tank atty is due to suction created when you draw. Slow and easy draws prevent some of the flooding.
If you think about it, vacuum plays a part in feeding as well as the wicking. When you draw, the air pressure around the coil and wicking drops slightly. If the tank is full, the air bubble in the tank is small and won't allow as much expansion. Just before the tank is empty, there's a larger bubble inside the tank that can expand more, allowing more juice to feed into the wick. A good hard draw at the end of a tank can result in a flood.