The dramatic differences between the results of Euler and Runge-Kutta integration are rarely as clear as they are in this chapter. For most models of social systems the different techniques do not lead to dramatically different results.
For physical systems, in which the interrelationships are exact and based on physical laws Runge-Kutta integration is almost always preferable. The one exception to this rule is for models such as the Thermostat model in which we have explicitly introduced discrete time concepts. If you use any discrete time concepts, especially any of the DELAY functions, you should probably stay with Euler integration.