Headphones are capable of some very effective left right "imaging," iand repruding subtleties of ambience, in many respects better than speakers. However externalization , i.e. the pereception of sound at a distance is more problematic because the headphone signals come from a space very close up to your ears. In this respect at least speakers have the advantage since they are some distance from you.
HEADPHONE VS SPEAKER LOCALIZATION
Speakers create "phantom channels" of signals whereby, for example the left channel feeds the right ear and vice-versa with a slight time delay. Thus you get 4 channels of sound from 2 speakers, two of them time delayed and which will interefere with the two correct signals. These phantom channels are complete artifacts and hence unnatural, compared to headphones which provide a pure left and right channel signal to the correct ear.
While you may think you are geting good spatial localization with conventional speakers, you should hear the sound when correction is made for the phantom channel artifacts. Some years ago Polk produced a series of SDA speakers which did this, with a fair degree of success. The images they produce are almost tangible by comparison with conventional stereo speakers.
Thus with headphones you are getting a more pure stereophonic signal.
MICROPHONE ISSUES IN SPATIAL REALISM
However, the realism of the image depends significantly on the nature of the recording. The signals picked up by 2 or more microphones used in recording may or may not be the same as your own ears would hear if you were in the listening situation. Generally they will not because the mics are spaced differently than your ears are spaced. Also, much music is multi tracked and micked, and creates a wholey synthetic stereo image. The extent to which it sounds real on either speakers or phones is a matter of the skill of the sonic engineers.
The best images will be obtained with "dummy head" recordings, where 2 mics are placed on a dummy head (or real head for the matter, I used to make my own such recordings with Sony's pro portable cassette machine and 2 small condensor mics clipped on my own ears.) The spatial realism of such images can be quite uncanny.
What tends to be still missing is "externalization," ie. the perception of sounds as occurring in a real space oustide of one's head. I recall in the notes of Sennheisser's old lp of dummy head recording, the claim that many people still perceive even such good recorded sound as being located somewhat to the rear of the listener. I certainly feel this is a problem with most headphones. And for the simple reason that the headphones drivers are somewhat toward he rear of the head, because that's where your ears are. Your brain is still strongly registering the true location of the source of the auditory signal.
PHONES USING EXTERNAL DRIVERS SUCH AS THE STAX SIGMA AND AKG1000
I agree with Duggeh about the Stax Sigma being able to partially get around this problem, for the simple reason that the drivers are mounted ahead of the ears (and I believe this is also true of the AKG K1000). In my own listening, I prefer the 007A for its sheer good sound and ability to register detail, but the Sigma/404( a modified Stax Sigma, using the later built Stax 404 drivers and cable) is a close second. It has a similar sonic signature but an openness and airiness of sound that almost no other phones have except the regular Sigmas and probably the K1000.
LATERAL SPATIAL LOCALIZATION vs DEPTH
The long review by darthnut makes some interesting observations about some phones and makes an interesting argument for auditory depth perception based in part on an analogy with what are termed in experimental psychology "monocular depth cues" i.e. cues or stimuli to distance which one can perceive with one eye, i.e. not relying on stereoscopic vision.
I think there is some truth in his observations but I would point out that the literature on auditory perception shows little evidence of any particularly acute auditory sense of depth as opposed to lateral spatial perception which can be quite acute. (Similalrly there is little evidence of any particularly good auditory perception of height.)
Many of the stimuli of distance he discusses are also inherently ambiguous, thus he claims that softer sounds are perceived as being further away. Why not just being softer (less loud) but at the same distance?
Lateral perception based on stereo cues is far more exact. Sounds producing an interaural arrival time difference are pretty unambiguosly located in a specific direction around the head. My point being that headphone listening is primarily about stereophonic spatial localization. Whne this is done accurately as is so by most phones, then sonic ambience tends to fall into its correct place/space too.