One thing that headphones have going for them verses speakers is that unlike speakers, their overall frequency response is not influenced by the room, or by dispersion characteristics. The same model of speaker can sound quite different in different rooms because only a fraction of the direct output from the speaker is reaching the listener's ears - the rest is indirect sound via the room (unless your room is an anechoic chamber). Also, two speakers with otherwise identical on-axis anechoic frequency responses can sound dramatically different in a room due to the speakers having different dispersion patterns over their frequency ranges. One of the speakers might have, say, much more off-axis high frequency energy than the other, which when the total direct & reflected sound reaches the ear in an actual room, that speaker will sound like it has stronger highs.
With headphones, any differences in their sound quality will be almost totally due to the actual frequency responses of the driver unit.