Neural network architecture design requires making many crucial decisions. The common desiderata is that similar decisions, with little modifications, can be reused in a variety of tasks and applications. To satisfy that, architectures must provide promising latency and performance trade-offs, support a variety of tasks, scale efficiently with respect to the amounts of data and compute, leverage available data from other tasks, and efficiently support various hardware. To this end, we introduce AsCAN---a hybrid architecture, combining both convolutional and transformer blocks. We revisit the key design principles of hybrid architectures and propose a simple and effective \emph{asymmetric} architecture, where the distribution of convolutional and transformer blocks is \emph{asymmetric}, containing more convolutional blocks in the earlier stages, followed by more transformer blocks in later stages. AsCAN supports a variety of tasks: recognition, segmentation, class-conditional image generation, and features a superior trade-off between performance and latency. We then scale the same architecture to solve a large-scale text-to-image task and show state-of-the-art performance compared to the most recent public and commercial models. Notably, without performing any optimization of inference time our model shows faster execution, even when compared to works that do such optimization, highlighting the advantages and the value of our approach.