I've tried the LCDi4 three times so far, but it just doesn't fit my taste. And given that I'm listening to electronica, I can say that I much prefer the bass presentation of the KSE1500 over the i4. The latter might be able to produce more volume undistorted, but for the level I listen at the KSE is more than capable of producing satisfying bass, clear, deep and powerful. Furthermore I dislike the upper mids presentation of the i4, something thats just excellent with the KSE.
The i4 looses what I really value with the Shure: isolation. I often use the KSE1500 while working at a cafe, where the i4 would be useless without turning up the volume too much. At home I mostly use over-ears, but the i4 was just plain uncomfortable to me, so I would not use it there as well.
I never use the KSE1500 on the go, its just too big and clumsy with its amp. On the other hand in the underground the SE846 works just fine, giving me about the same isolation and the option of a Bluetooth connection. So besides me not liking the sound signature of the LCDi4, I simply see no use case for me. I don't like in-ears too much from a comfort point of view, but the KSE1500 is just so excellent sounding that I even use it at home sometimes. Over the past few months owning it, I'm more and more thinking, its the best headphone I've heard so far.