Focusing on large-scale vehicular ad-hoc networks (VANETs), we consider the interplay between single-hop channel models and large-scale network connectivity. Building on a realistic urban traffic simulator, we progressively increase the sophistication of the wireless link while evaluating the resulting connectivity profiles. Our results show that large-scale VANET connectivity, whose understanding is paramount towards the development of protocols and applications for this class of networks, is equally influenced by the choice of model and by the fine-tuning of its key parameters. Analyzing the distributions of both node degree and the duration of connection, we conclude that (a) as far as large-scale node degree behavior is concerned, a complex shadow fading environment is well approximated by a simpler and more tractable unit-disk model and, (b) unit-disk models allow longer connections than other models.