You know what, there may be three factors at work here.
1. quad-segment jack not quite working with stereo sockets. You KNOW when this happens. The sound is way off as you say. On some sockets wiggling the jack a bit solves the problem, on others not so.
2. inherent difference between the SHH3580 and SHE3580. I found that even with the SHH plugged into my phone the bass is leaner. Not exactly LEAN; in fact without EQ the bass on the SHH may be just the right amount for many people, but the subbass extension seems to be less. With the SHE3580 I like it best with the midbass to subbass EQed down, but I like how there's so much headroom for me to bump the subbass back up if I want more. With the EQ settings for the SHE3580 dialled in, plugging in the SHH sounds good, but with the SHE3580 it sounds like somebody turned on the Mega Bass or the stereo expander--except better, because it's just how the phones sound.
3. break-in. The SHE3580 I'm using has had months of break-in, some of it on accidentally high volumes. Nevertheless, another pair of SHE3580 that has seen little use just like the SHH(and is blue instead of black) sound very similar to my primary pair, to the extent that I can plug them both into a Y-splitter, put one bud from each set into each ear and not feel any imbalance. If I do this with the SHE3580 vs the SHH3580 I get the feeling that the sound from the SHE3580 side is "bigger".
So, the short story is: if you're using these primarily for music, I recommend getting the SHE3580 over the mic'd SHH3580, especially if you want your bass heavy and extended.
Another spanner in the works is the SHE3575, which is another mic'd version that looks even more similar to the SHE3580 than the SHH (notice the strain relief on the earbuds of the black SHH3580 are red; on the black SHE3580 and SHE3575 they're black). I wonder if the sound of the SHE3575 would be more similar to the SHE3580 than the SHH too? On the other hand the silicone tips on the SHE3575 are coloured instead of the clear tips on the SHE3580 and SHH3580.
Gah, wondering whether the minor colour differences in these models makes the sound different makes me feel like a stupid fashionista On the other hand, these do look colourful and stylish in a minimalist way. Then again, my primary pair is black and I do believe that