Some of the transistor H-Bridges can loose 2V per transistor, so with one at the top and one at the bottom your voltage loss is likely to be in the order of 4V.
That is not true of the Adafruit V2.3 motor shield, mentioned in the OP. That shield has TB6612 MOSFET drivers.
From the TB6612 data sheet, the "output saturating voltage" drop is typically 0.5V at 1 A current draw.