The surging development of Artificial Intelligence-Generated Content (AIGC) marks a transformative era of the content creation and production. Edge servers promise attractive benefits, e.g., reduced service delay and backhaul traffic load, for hosting AIGC services compared to cloud-based solutions. However, the scarcity of available resources on the edge pose significant challenges in deploying generative AI models. In this paper, by characterizing the resource and delay demands of typical generative AI models, we find that the consumption of storage and GPU memory, as well as the model switching delay represented by I/O delay during the preloading phase, are significant and vary across models. These multidimensional coupling factors render it difficult to make efficient edge model deployment decisions. Hence, we present a collaborative edge-cloud framework aiming to properly manage generative AI model deployment on the edge. Specifically, we formulate edge model deployment problem considering heterogeneous features of models as an optimization problem, and propose a model-level decision selection algorithm to solve it. It enables pooled resource sharing and optimizes the trade-off between resource consumption and delay in edge generative AI model deployment. Simulation results validate the efficacy of the proposed algorithm compared with baselines, demonstrating its potential to reduce overall costs by providing feature-aware model deployment decisions.