Here's a very good article on the differences between mixing on headphones and speakers.
Mixing On Headphones
This SOS article was written in 2003. It's very old and might not represent the state of headphone technology and it's uses vs open speaker monitoring.
Today, more and more people use headsets than anytime before. i-phones i-pads and every different type and kind of app available have headset adapters. Also, the disciplines of monitoring music projects today have changed a lot since 2003 when this article was written. With the sale of home audio listening devices down (stereo components, affordable speakers etc..) and home speaker technology getting more and more expensive and inconvenient to listen on, the average person who loves their music might only afford a good headset and amp for listening.
My projects are mixed with both audiophiles in mind. One way of mixing is in no way better or worse than the other way. It's very subjective today. 20 some-odd years ago, I only used my cans for critical listening and recording live instruments and vocals where I needed to hear distinctions and separation between frequency characteristics and level degrees. Though I still like to use both systems for monitoring tracks, I believe you can produce a whole album on a quality set of cans and a very good HP amp.
In consideration that, many more people are listening to music on their ear buds and headphones today than ever before, monitoring technology had to keep up with the demands of the listener.