Many factors come into play here. Rider weight, gearing, the power output of a particular engine and how easy the clutch is to control. First you have to consider this basic fact. It isn't a motorcycle. It is a motorized bicycle with a limited horsepower engine and an imperfect clutch design. They are designed to be pedal assisted and that usually means that from a dead stop you need to pedal to take some of the pressure off the clutch pads and engine to overcome inertia.
A bike with a large rear sprocket, low geared, will be easier to start from a stop than one with a smaller, higher gear sprocket. Many owners who have done no clutch linkage modification will find it difficult to 'slip' the clutch with the handlebar lever, however there are things that can be done to allow slow, easy application of the clutch making a dead stop start possible but it still puts undue wear on the clutch components.
Even with a centrifugal clutch, helping the bike to get rolling with the pedals is a good way to increase clutch life.
Horsepower and torque are also considerations. The Mopeds you mentioned might be 50cc but they might also produce more 'umph' than the standard, unmodified China Girl.
Tom