Dual Power Management with MOS
Regarding the drop between the supply and the output, it definitely comes from the \$R_{DS(on)}\$ parameter of the MOSFET. When the MOSFET is conducting, there is actually a resistor equal to \$R_{DS(on)}\$ between the drain and the source. This is usually small, but of course if the current flowing through the MOSFET is high, it creates this drop that you have observed.

What you mentioned in your comment, that there is a difference in the drop when you connect V1 with V2 and when not, this is also logical: consider what happens when you connect them together. Then you actually have both R8 and R9 as a load for the supply that is active and thus the total load is 1 Ohm instead of 2 Ohm! Thus more current is flowing through the transistor and more voltage drop is created!