This chapter compares two computational frameworks developed over the last decade to support investigations into the emergence and use of language, Fluid Construction Grammar (FCG) and Embodied Construction Grammar (ECG). Both of these representational formalisms are rooted in the construction grammar tradition, sharing basic assumptions about the nature of linguistic units and the crucial role played by contextual factors. Nonetheless, they have arisen from different perspectives and with different goals: FCG was designed to support computational language game experiments that address the evolution of communication in populations of robotic agents, while ECG was designed to support cognitive modeling of human language acquisition and use. We investigate how these differing emphases motivated different design choices in the two formalisms and illustrate the linguistic and computational consequences of these choices through a concrete case study. Results of this comparison sharpen issues relevant to computational construction grammar in general and may hold lessons for broader computational investigations into linguistic phenomena.