When would you choose a synchronous bus over an asynchronous one?

Choose synchronous (a shared clock) when you want to avoid the accuracy burden of matched timing, support a wide or variable range of speeds, or clock devices that can't keep precise time on their own. Because the clock travels with the data, a synchronous bus like SPI or I2C works at whatever rate the slowest participant tolerates, can be paused or slowed arbitrarily (I2C even lets a slave stretch the clock), and doesn't care about the devices' internal oscillator accuracy, useful for cheap sensors with imprecise clocks. You'd choose asynchronous (UART) when you want to save the clock wire and connect over longer or simpler links where running an extra synchronized clock line is impractical, accepting that both ends must hold accurate matched baud (within a few percent) and that there's no built-in flow-rate negotiation. In short: synchronous trades a wire for timing robustness and speed flexibility; asynchronous trades timing precision for one fewer wire.