By the criteria stated in the original question, the steady state pressure at the point of pump suction and the point of pump discharge will be identical for both schemes. Therefore the pump differential head will be identical for both schemes. You do not need more pump head for the vertical loop piping on startup as long as the discharge line is kept full of liquid.
The original question is posted in the 'Student' section so I will answer as if the original poster were an engineering student. The problem is a classic fluid flow problem. Determine pressure drop in the discharge line for both schemes and compare the results.
P(end)= P(start) - friction loss- fittings loss -component loss + elevation (start-end) + pump head
Solve the equation for P(start) at the point of pump outlet. P(end) is the point of the line at the final destination. Elevation (start-end) is zero for both schemes. Pump head is zero for both schemes since there is no pump in the discharge line. The attachment with the original question states the assumed friction loss in both schemes to be the same: "Discharge pipe friction loss = 0.2 bar (loss assumed same as straight length, for ease understanding, in real loss will be more than straight length because of bends)" This assumption is an artificial constraint and may not 'ease understanding' for readers since it conflicts with real world experience and application. If the discharge line is not kept full of liquid, the 'same pressure drop in the line' assumption is even more misleading.