We compare two strategies for lossy source description across a pair of unreliable channels. In the first strategy, we use a broadcast channel code to achieve a different rate for each possible channel realization, and then use a multiresolution source code to describe the source at the resulting rates. In the second strategy, we use a channel coding strategy for two independent channels coupled with a multiple description source code. In each case, we choose the coding parameters to minimize the expected end-to-end distortion in the source reconstruction. We demonstrate that in point-to-point communication across a pair of non-ergodic channels, multiple description coding can provide substantial gains relative to mulitresolution and broadcast coding. We then investigate this comparison in a simple MIMO channel. We demonstrate the inferior performance of space time coding with multiresolution source coding and broadcast channel coding relative to multiple description codes and a time sharing channel coding strategy. These results indicate that for non-ergodic channels, the traditional definition of channel capacity does not necessarily lead to the best channel code from the perspective of end-to-end source distortion.