You have to further define "high-end" to get more specific answers to your question. Some properties of sound quality, such as resolution and channel separation, will almost always be better when using headphones, while visceral impact, sound stage, and imagining will almost always be better when using speakers. The problem with proclaiming the superiority of one over another is that the determining factor of such superiority is one's own listening preferences and sound priorities; one who craves soundstage in music will be generally more drawn to speakers, while one who enjoys picking out individual instruments within a soundstage will more likely embrace the resolving abilities of a headphone driver. So, in short, there really isn't a direct answer to the question you have proposed above; like most things in audio, personal taste is the one and only deciding factor which controls your likes and dislikes of general equipment.
Regards,
Nick