HE400i has a response that is objectively better but subjectively people tend to not like it. It also needs more amplification, and those amps you can get your hands on won't really cut it.
HE400S response is technically inferior but subjectively has broader appeal, if not the HE400S by itself include popular headphones that have a similar response curve (HD600, K702, etc). Basically it sounds more like an older planar or a dynamic headphone driver, albeit with less driver distortion than a dynamic driver. It's also got a much higher efficiency - Q1 Mk2 will be more than enough to power it fully. Past that if you go higher up the chain on amps you're just going for lower distortion and noise, not for want of more power. HE400i will need rouhgly 4x the power to play at the same output level as the HE400S.
