Nonhuman primates have smaller brains, and humans have large brains and advanced technology. how does the birthing process differ?

Non human primates have smaller brains; therefore the birthing process differs by being shorter and less painful. 
There is no known living primate has as much difficult giving birth as human beings. The principle reason giving birth is harder for humans is the size of the infant's head compared to the size of the pelvic opening that it has to pass through during birth. However, the size of the pelvic opening is limited by the mechanical demands of walking upright. 

Giga is the second highest prefix on the normal scale, the first is terra.