To be honest, I think it depends on the devices in question. I generally prefer dedicated devices to multi-purpose devices mainly because of the loss of functionality in multi-purpose devices. That's the main reason why I still refuse to get a smart phone; the only thing I use my phone for is to call and text. I prefer cameras to take pictures, laptops or tablet pcs to surf the Internet... Stuff like that.
At the same time though, there are some devices that are just that good at multi-purpose devices. Like my iPad for example; I can use it as an e-reader (hate the glare, but I have no choice seeing that it's the only reader I actually can use), to surf the Internet, play games (the games are generally cheaper too). I've even taken to storing my music collection there too, because it's easier to sync that manually transfer files like my MP3 player.
But it still sucks as an e-reader though, which is why I doubt dedicated readers are going to out of fashion.