Negative feedbacks and incoherent feedforward loops are known to give rise to a pulse in response to a step change in the input. In this article, I present a study of composite motifs made of coupled feedback and feedforward loops, acting via different regulatory mechanisms. In these motifs, the effect of input and output on the controller is realized via either an AND-gate or an OR-gate. Using a simplistic model of gene expression and a common parameter set, I have studied the effect of global parameter variation on the dynamic and steady-state properties of different motifs, in response to a step change in the input. These metrics include steady state gain, response time, overshoot, peak time and peak duration. For the motifs with a negative feedback component, it can be seen that AND-gated motifs show a "feedforward-like" property whereas the OR-gated motifs show a "feedback-like" property. Motifs with a positive feedback component show hypersensitivity of gain, to parameters. Overshoot correlates negatively with peak time whereas peak duration correlates concavely with peak time, a property that is also observed for uncoupled feedback and feedforward motifs. This indicates that this relationship between overshoot, peak duration and peak time, seems to be a universal property of pulse-generating motifs.