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We make a comparative analysis of two different multilayer organic light-emitting diodes (OLEDs), one of which has an emitting layer (EML), and the other has a carrier transport controlling layer (CTCL) embedded between a hole transport layer (HTL) and an electron transport layer (ETL). The key differences between them lie in the carrier mobilities (relatively low for EML but high for CTCL) and energy levels of the middle layer. An in-depth numerical analysis has been done to provide guidelines for the design of trilayer OLED structures, especially in the context of mobility and energy level offsets. Furthermore, we focus on the transient response and carrier charge and discharge dynamics of those devices. Other than the HTL/CTCL/ETL structure, the transient current balance of the HTL/EML/ETL structure is shown to be much affected by the energy level offsets at the organic/organic interfaces due to the slow carrier dynamics in the EML. It is also demonstrated that the electroluminescence (EL) delay upon turn-on is mainly determined by the electron transport passing through the ETL and further EML, while the fast EL decay upon turn-off is by the rapid discharge of the abrupt accumulation of carriers at the organic/organic interfaces.