1ton,
I will presume that your question refers to external tooth pumps vs. internal tooth pumps rather than whether external timing gears are involved.
Usually, pumps configured with two meshing external spur gears as the pumping elements offer the lowest initial price, and they are usually reasonably durable. One characteristic of this arrangement is relatively abrupt opening and closing of the void spaces that transport the pumped fluid from the low pressure region to the high pressure region. This can result in significant local accelerations of the fluid and significant noise from the high frequency pressure pulsations.
Pumps configured with a combination of meshing internal and external gear teeth such as "Gerotor" and "cresent" pumps provide less abrupt opening and closing of the void spaces. Because of this, local accelerations of the fluid are more gentle, the NPSHr is lower, and the operating noise level is lower. (I've experienced cases where "Gerotor" pumps replaced "cheaper" external gear pumps and the noise level dropped so dramatically that the pump ceased to be the dominant local noise and the new pumps were functionally silent--their operation simply could not be heard.) These types of pumps are likely to be more sensitive to damage from solid debris in the pumped fluid, and they are more sensitive to the pumped fluid for lubrication.
With reasonable filter protection for the pumps, all types can provide reasonably trouble free service. If noise is a concern, then I would use a "Gerotor" style pump.