Even though earbuds are more convenient to use (esp. if you want to carry them around), I like headphones much better (esp. noise-canceling headphones). Earbuds are louder and more damaging to your hearing -- the strength of sound is proportional to the square of the distance, so if the sound source is 3 times closer to your ear-drums when using earbuds over headphones, then the strength of the sound is about 9 times as strong (32=9). Also the sound quality is much better with headphones than it is with earbuds, esp. in the lower ranges. If you notice, most DJs (as well as recording studios) will use headphones over earbuds in order to hear all of the different layers of sound. Finally some headphones are noise-canceling which means that the outside sound is lessened allowing you to reduce the music's volume (since the music through the headphones won't have to compete with the outside noises) while at the same time allowing you to hear the full range of the music.
Having said all that, most of the time I'm listening to music at work, and there I tend to use earbuds for the convenience factor.