Earbuds require less power to use for the phone itself. Headphones has better sound. It's your decision which is more important to you. Good earbuds are hard to find. It also depends on what kind of controls you'd like with the purchase.
This was what I purchased. The Monster iSport Bluetooth sports earbuds
PROS:
5+hrs of listening time
sweat resistant when working out
BT, wireless so you can almost roam around your house
built in wings, does not fall out
CONS:
No foam tips included. (Foam can form fit to your ear canal for better comfort and stays in better, seals out noise better. you can hear your heart beat)
lacks bass
need to recharge