ADX5000's has the better bass response out the box. I boost on my set via my RME ADI-2 and Lokius to meet my preferences. I still like the HD800S's clarity. It's sharper and a bit more focused than on the ADX5000's. For everything else I prefer the ADX5000's.
The ADX5000 definitely wants to rival the HD800S for the best dynamic headphone out there. It definitely has better looks and build quality. It is also lighter.
The HD800S looks and feels a bit cheap, but I think it is also rugged, can withstand a few drops on the floor, because it's sturdy plastic. It might even survive if a child or a woman sits on it accidentally, or a dog takes it and chews it. Or your wife gets hysterical and throws it at you. If it breaks probably Sennheiser can send you spare parts. The ADX I think, if it gets some abuse will deform and bend and paint may chip off. So it's nicer, but you need to guard it more. Also the ADX is more of a magnet for thieves, the HD800S may be mistaken for a cheap headphone, not worth putting in the bag.
Japanese engineering may be able to beat the German engineering.
The sound tough can be a tossup, some may miss the soundstage of the HD800S if they switch to the Japanese one, even tough in some areas the ADX can beat the Sennheiser. Not everybody is so wealthy to own both.
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