For the most part, unless you find a dog of a headphone -- and they certainly do exist -- the sound will likely be adequate for metal detecting. And whatever you use, you will get used to hearing those headphones; when you switch to something else, they will sound 'funny' at first, because you've learned the nuances of your previous set. Really, what you want to consider is
1. Cord or cordless: Corded headphones are far more plentiful and never need batteries. Cordless phones get that annoying, tangling cord out of the way, but need charging and are often more expensive. Many also have a small delay that make them next to useless for detecting.
2. Type of Headphones: Basically in-ear (earbuds), on-ear (smallish pads that sit on top of the ear), or over-ear/circumaural (completely surround ears.) This is a matter of both personal preference (comfort) and affects the sound you hear. For non-earbuds, the headphones can also be open or closed backed. Open means some sound bleeds through and closed means they are completely sealed.
Speaking only of my preferences, I hunt a lot in brush and foliage and the cord was always getting tangled or jerking my head, and thus I prefer wireless. I don't like earbuds and prefer a large set of circumaural headphones -- they also double somewhat as ear warmers in a harsh wind or in late autumn hunting. And since I don't like to be completely oblivious to my surroundings, I also like an open-backed set that doesn't entirely muffle all outside noise. I found the perfect match in a pair of Sennheiser HDR 180 phones. The transmitter is a bit on the large size, but Velcros just fine to the back of the Xterra control box.
For wireless, any phones with "KLEER" technology like these will work better than cheap bluetooth sets (stay away in general), and there are many good options for wired headphones that people can recommend, from dirt cheap to super expensive.
