H bridge design for bipolar motor
The second circuit can work, but only under circumstances which are extremely unlikely. The problem is that


  This design doesn't require the additional 2 N mosfets from the first
  design.


but it does require that the two control lines swing between 0 and 9 volts.

Let's say that your MCU outputs swing between 0 and 5 volts. Then the two p-type MOSFETs Q1 and Q2 will have gate voltages from gate to source, of -4 and -9 volts. In neither case can you guarantee that those FETs will ever turn off. Then whichever n-type is turned on will cause a short from 9 volts to ground.

And that will not make you happy.

I am, of course, assuming that your MCU pins do not go from 0 to 9 volts. Correct me if I'm wrong.