Convolutional neural networks are utilized to solve increasingly more complex problems and with more data. As a result, researchers and practitioners seek to scale the representational power of such models by adding more parameters. However, increasing parameters requires additional critical resources in terms of memory and compute, leading to increased training and inference cost. Thus a consistent challenge is to obtain as high as possible accuracy within a parameter budget. As neural network designers navigate this complex landscape, they are guided by conventional wisdom that is informed from past empirical studies. We identify a critical part of this design space that is not well-understood: How to decide between the alternatives of expanding a single convolutional network model or increasing the number of networks in the form of an ensemble. We study this question in detail across various network architectures and data sets. We build an extensive experimental framework that captures numerous angles of the possible design space in terms of how a new set of parameters can be used in a model. We consider a holistic set of metrics such as training time, inference time, and memory usage. The framework provides a robust assessment by making sure it controls for the number of parameters. Contrary to conventional wisdom, we show that when we perform a holistic and robust assessment, we uncover a wide design space, where ensembles provide better accuracy, train faster, and deploy at speed comparable to single convolutional networks with the same total number of parameters.