The first diagram is the one that works very well in my TVR Griffith even though the overflow tank is located lower than the swirl.
The air bubbles present in the circuit accumulate at the top of the swirl and are expelled into the overflow tank when the liquid expands under the effect of heat during the first heating of the engine. It is the expansion of the liquid that creates the delta P between swirl and overflow tank. This air then accumulates in the upper part of the overflow tank and escapes if the pressure becomes higher than that of the cap. If there has been too much water poured into the circuit, the overflow also escapes. When it cools only liquid is pushed back into the swirl by the pressurized air at the top of the overflow tank since it is connected to its lower part, so there is never any air in the swirl .
In the second diagram connecting the overflow tank to the pump suction creates some radiator bypass, even if it is limited by the diameter of the pipes, and therefore slightly decreases the flow through the radiator. In addition, the swirl being connected at the top of the header, the air can be sucked into the swirl when the liquid cools and retracts.
But apparently both work well and it's up to each individual to choose.