Just going to answer OP's question:
Beyond audiophile snobbishness and pedantry and pride and whatnot, the Beats in any iteration are a marketing ploy. I would know. I just got what is ostensibly an authentic Detox from an uncle. Guy has a Cambridge Audio -> 12AX7+KT88 Duntonic -> JBL floorstanding rig, so I thought he would know better. It's the thought that counts though.
Let me assure you that the Detox is a lumbering piece of overhyped marketing trash that in my opinion, tangentially misses the mark at which one could find it possible to sue for misrepresentation. Out of my laptop (it has a decently clean Conexant integrated soundcard - the Beats deserve nothing more for a source), testing it with 24/96 recordings of Mozart's Violin Concerto No.4 performed by Marianne Thorsen and the last movement of Beethoven's Symphony No.9 under the Berlin Philharmoniker and Claudio Abbado, I found cans that could not even hold a candle to the M50's, which I hated. Seriously, for that price, I pine for a top-class closed headphone such as the AT woodies, Thunderpants or even the Z1000 and SRH940. The mids would recessed, as soulless as the marketing behind it, with highs that besmirch the purity of the violin concerto aforementioned. Soundstage would be obviously larger than stock earbuds to the uninitiated due to the inordinate amount of backwaves and echos from a casing designed to look as pretentious and ridiculous as possible. The paddings are thick, but are obviously pleather - unacceptable for the price. My father was shocked at the quality of the Beats too. Guy knows his hi-fi (he thrashed everything short of a HD800 in terms of resolution), and believed my ranting afterwards.
tl;dr I gave them to my brother.
I would also kill for the Z1000 in exchange for the Detox LNIB. All documentation present. I am sure some Headfiers would be tempted....