The K712 that mad reviewed was the one I loaned him. I also have an E12, which doesn't particularly add warmth (pretty colorless unless you use the bass boost switch).
The K712 is a gentler u shaped freq-curve (graphs available at inner fidelity and headroom), with elevated/forward bass that is below the point where bass usually starts to distort, it dips as it reaches the mids but mostly stays near the neutral point, and then a bit of energy/sparkle to the treble. It HAS stronger bass, and it is engaging in a way that excites me but doesn't do things too much to become irritating, so IMO it's a longer term headphone to have (my current "on a desert island") than the more colored X1.
I used my Mixamp 5.8 with my K712 plugged straight in, often in fact, it sounds very good. The Mixamp has relatively close to the output power of an iPod Classic, so loudness isn't a problem, but double amping just kindof finishes off the weight of impact and helps refine & control sound reproduction.
Before the K712, I was happy with the Q701, which is very similar, for about a year and a half.