It depends on what you get. Some headphones are better than others, both for wireless and wired. For mono Bluetooth (in the car) I like the Jawbone ICON; the newer HD version is supposed to let you pause and play, which is lacking on the original. If this is for driving, I'd definitely go Bluetooth, the wires always get tangled and caught on stuff for me, and of course you can only use one ear.
For stereo Bluetooth, I recommend Plantronics BackBeat 903+. I'm wearing them right now. What I like is that the two earpieces are connected by a thin cord that goes around the back of your neck; some of the others I've had had hard plastic that was not as comfortable. They also have good battery life and volume. The small mono ones like Jawbone usually have small batteries, so have to be recharged more often, but charge quick.
They've both been out for a long time, so you can find them relatively cheap on Amazon, but they're still high quality. There are plenty of others. You want to make sure that they have A2DP, so that you can play music from your iPhone. It also helps if they have AVRCP so they have audio controls. Those Bluedio ones are really cheap, so there's not much risk in trying them out. Apparently the manufacturer also makes higher-end over-the-ears Bluetooth headsets and such.
As for wired earphones, make sure that they're made for iPhone, so they have audio controls and a mic for phone calls.
You also have to consider whether you want the kind that go in the ear canal, sit on the outer ear like iPod/iPhone earbuds, or cover the ears. You didn't say how or where you intend on using them or any other preferences. There is a huge variety of headphones, with prices from single digits to hundreds of dollars.