Not an aircraft engineer or designer, but gear pumps give a smooth constant delivery. Diaphragm pumps give a pulsed delivery, and rely on a rubber/nitrile diaphragm, which can perish or develop holes and leaks. A gear type can give a much larger volume flow and higher delivery pressure.
Depending on the fuel system and engine demand; each type has its uses. So a small carburettor engine might be fine with a diaphragm pump, whereas a large and/or fuel injected engine would probably use a gear pump, and large turbine engines certainly do.