LSTMs are on their retour in my opinion. They are a hack to make memory in recurrent networks more persistent. In practice they overfit too easy. They are being replaced with convolutional networks. Have a look at the latest paper from Facebook about translation for more details.
The way I see it, the difference is that with CNN you have fixed maximum timeframe in which knowledge about world is preserved, while LSTMs and RNNs in general do not impose such restrictions. This makes them better suited for some applications.
