Basically, I use a mobile theme when I want to reduce the amount of data downloaded (or instance, smaller images). Otherwise, I just use a responsive theme to ensure a consistent 'feel' between devices.

There isn't a whole lot of difference between the two. Really, it all depends on how quickly either theme loads. Some responsive themes are lighter than others and so they load more quickly. The problem with a purely mobile theme is that it is like creating your website a second time, which takes a lot more time. Responsive themes are much more efficient because they are intended to render your site across many different device and screen sizes.

Due to today's diversity of how people are using the web, responsive themes are the way to go.