They make a difference for me. I found myself being able to ride longer and more comfortably with cycling shoes. My legs did not hurt as much and my avg speed was able to increase as I had a much better pedal stability and consistent cadence.
For those that have bike shoes - do they really make a difference? I have 13EEEE feet - finding shoes in that size just seems like more effort than it's worth. I use platform pedals so I don't care about cleats. Typically my biking shoes are the ones that I don't want to walk around in public anymore with, seems to be one area to save dough (I am super tough on shoes, if they last me a few months that's impressive). Not racing but like to ride long distances.